# Thread: Distance, Rate, and Time... help?

1. ## Distance, Rate, and Time... help?

"A canoeist paddled 2 hours with a 3 km/h current to a fishing site. The return trip against the same current took 6 hours. Find the speed of the canoe in still water."

I'm supposed to solve this problem with two variables and write two equations, but I can't seem to figure out how to do that. If anyone could lend me a hand, it would be much appreciated.

2. Originally Posted by firefly_senshi6
"A canoeist paddled 2 hours with a 3 km/h current to a fishing site. The return trip against the same current took 6 hours. Find the speed of the canoe in still water."

I'm supposed to solve this problem with two variables and write two equations, but I can't seem to figure out how to do that. If anyone could lend me a hand, it would be much appreciated.
Assume the canoe travels at a speed v in still water.

The trip downstream was with the current, so according to an observer on the shore the boat moved with a speed of v + 3 km/h and travelled a distance of x km in 2 hours.
$\displaystyle v + 3 = \frac{x}{2}$

The trip upstream was against the current, so according to an observer on the short the boat moved with a speed of v - 3 km/h and travelled a distance (again) of x km in 6 hours.
$\displaystyle v - 3 = \frac{x}{6}$

We want v, so solve the first equation for x:
$\displaystyle x = 2(v + 3)$

Insert this value of x into the second equation:
$\displaystyle v - 3 = \frac{2(v+3)}{6}$

Now solve for v. I get v = 6 km/h.

-Dan

3. Ahh, thank you so much!! It makes sense now.
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