Question

Two cutters travel in the same direction down a river at different] speeds. When they come alongside one another, a life-buoy is thrown out from one of the cutters. Some time afterwards, both cutters turn around simultaneously and travel back towards the spot where the life-buoy was thrown, the relative speeds being the same as before. Which of the cutters reaches the life-buoy first? Solve this problem also for the cases in which the cutters come alongside (a) travelling upstream, (b) travelling towards one another. 

Answer 1

Answer: In all three cases, the cutters arrive at the buoy simultaneously.

Explanation:

The speed of the current affects the motion of both cutters in the same way and cannot change their relative positions, and we may neglect the current and consider the motion of the cutters and buoy relative to the water only. The distances travelled by the cutters relative to the water in a time t until they turn around is S₁ = v₁t and S₂ = v₂t. The cutters, returning to the buoy at their previous speeds v₁ and v₂ should take the same time in travelling the distances S₁ and S₂ to the buoy as they spent travelling away from it.