Question

a boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. what is the rate of the boat in still water?

Answer 1

Let b equal the speed of the boat in still water.
Let c equal the speed of the current.
Going downstream, we can write the equation:
$b+c=\frac{120}{3}$
which can be rearranged to:
3b + 3c = 120 ............(1)
Going upstream, we can write the equation:
$b-c=\frac{120}{4}$
which can be rearranged to:
4b - 4c = 120 .............(2)
Multiplying equation (1) by 4, and multiplying equation (2) by 3 we get:
12b + 12c = 480 ........(3)
12b - 12c = 360 .........(4)
Adding equations (3) and (4) results in the following equation:
24b = 840
$b=\frac{840}{24}=35\ mph$