data_source
stringclasses 1
value | prompt
listlengths 1
1
| ability
stringclasses 1
value | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
deepscaler
|
[
{
"content": "The pressure \\( P \\) exerted by wind on a sail varies jointly as the area \\( A \\) of the sail and the cube of the wind's velocity \\( V \\). When the velocity is \\( 8 \\) miles per hour, the pressure on a sail of \\( 2 \\) square feet is \\( 4 \\) pounds. Find the wind velocity when the pressure on \\( 4 \\) square feet of sail is \\( 32 \\) pounds. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] |
math
|
{
"ground_truth": "12.8",
"style": "rule"
}
|
{
"index": 124,
"split": "train"
}
|
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