Question

A motorboat going downstream overcomes a raft at a point A. 60 min later it turned back, and after some time it crossed the raft again at a distance $l=6$ km from point A. Then,

• A. Flow velocity of river is 3 km/h.
• B. Flow velocity of river is 4 km/h.
• C. Velocity of motorboat is 6 km/h.
• D. Velocity of motorboat is 9 km/h.

Answer 1

Answer: (A), (C), (D)

Velocity of motorboat is 9 km/h.

Velocity of river and boat be $V_r\&V_b$
Place the frame of reference on the raft. Since, raft is moving with the same speed as that of the river and the frame of reference is on the raft, the river is at rest in that frame of reference. In this frame of reference, the motor boat moving away from raft with a speed of $V_b$ for 60 mins and then returned with the same speed, so it takes 60 mins again for the boat to meet the raft. So, the total time is 2 hours. Given that, the raft has moved 6 km wrt ground in these 2 hours, so its speed is $\frac{6}{2}=3$ km/hr. Therefore, the speed of the river is also 3 km/hr. As you can observe, the speed of the boat did not matter until now, it can take any value.