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**Solution:**

Let v_{0} be the stream velocity and \( {v}’ \) the velocity of motorboat with respect to water. The motorboat reached point B while going downstream with velocity \( ({{v}_{0}}+{v}’) \) and then returned with velocity \( ({v}’-{{v}_{0}}) \) 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 then from B to C.

Therefore

\( \frac{\ell }{{{v}_{0}}}=\tau +\frac{({{v}_{0}}+{v}’)\tau -\ell }{({v}’-{{v}_{0}})} \).

On solving we get \( {{v}_{0}}=\frac{\ell }{2\tau } \).

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