Question

A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream.

Answer 1

T = time for downstream
t = time for upstream travel
T + t = 3 hrs 45 min = 15/4 hrs

Let $v$ be the speed of the stream.

For downstream, $T=\frac{15}{9+v}$

For upstream, $t=\frac{15}{9-v}$

Adding (1) and (2), $\frac{15}{9+v}+\frac{15}{9-v}=\frac{15}{4}\Rightarrow \frac{270}{81-v^2}=\frac{15}{4}\Rightarrow v^2=9\therefore v=3kmph$