A motorboat going downstream overcame a raft at a point A; τ=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.
Considering the given figure below.
Let v0 be the stream velocity and v′ the velocity of motorboat with respect to water. The motorboat reached point B while going downstream with velocity (v0+v′) and then returned with velocity (v′−v0) and passed the raft at point C. Let t be the time for the raft (which flows with stream with velocity v0) to move from point A to C, during which the motorboat moves from A to B and then from B to C.
Therefore
lv0=τ+(v0+v′)τ−l(v′−v0)
On solving, we get v0=l2τ=3km/hr.