Question

A motorboat going downstream overcame a raft at a point $A$; $\tau =60min$ later it turned back and after some time the raft is at a distance $l=6.0km$ from the point $A$. Find the flow velocity in $km/h$ assuming the duty of the engine to be constant.

Answer 1

Considering the given figure below.
Let $v_0$ be the stream velocity and $v^{\prime }$ the velocity of motorboat with respect to water. The motorboat reached point $B$ while going downstream with velocity $(v_0+v^{\prime })$ and then returned with velocity $(v^{\prime }-v_0)$ and passed the raft at point $C$. Let $t$ be the time for the raft (which flows with stream with velocity $v_0$) to move from point $A$ to $C$, during which the motorboat moves from $A$ to $B$ and then from $B$ to $C$.
Therefore
$\frac{l}{v_0}=\tau +\frac{(v_0+v^{\prime })\tau -l}{(v^{\prime }-v_0)}$
On solving, we get $v_0=\frac{l}{2\tau }=3km/hr$.