A swimmer and a freely floating raft are together at an instant in a river. The swimmer immediately swims upstream with speed u relative to water for time T, then turns instantly and swims downstream with the same relative speed. After turning, the time required to meet the raft again is:
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Question

A swimmer and a freely floating raft are together at an instant in a river. The swimmer immediately swims upstream with speed u relative to water for time T, then turns instantly and swims downstream with the same relative speed. After turning, the time required to meet the raft again is:

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G1 Physics · Accepted Answer

Use the water frame. The raft is stationary in this frame. During the first T seconds the swimmer moves a distance uT away from the raft. After turning, he approaches the stationary raft at speed u, so return time = uT/u = T. River speed cancels completely.