Question

A boat takes 4 hours to travel 37.09 km down a river, then 6.6 hours to return. How fast is the river flowing?

Answer 1

in first condition boat and the river flow are in the same direction so the relative velocity is

V = V_b + V_r

and hence

relative velocity = distance / time

( V_b + V_r ) = 37.09/4

V_b + V_r = 9.27............................(1)

in the second condition velocities are in opposite direction

hence  V = V_b  - V_r

V_b  - V_r = 37.09 / 6.6

V_b  - V_r = 5.62 ..............................(2)

by subtracting equation 2 from 1 we get

2V_r = 3.65

so V_r = 1.825

Hence the river flowing with 1.825 km / h