Question

A motorboat takes 5 hours to travel 200 km going upstream. The return trip takes 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

rate of motorboat: b
rate of current: c
So the rate the boat travels upstream is $b - c$, and the rate it travels downstream is $b + c$


`d = rt`

`200 = (b - c)\cdot 5`

`200 = (b + c)\cdot 4`

`b - c = 40`

`b + c = 50`

Adding these equations, we get:

`2b = 90`

`b = 45`

So

`c = 50 - 45 = 5`

Therefore the rate of the boat is 45kph, and the rate of the current is 5kph

Hope this helps :)