A boat went down the river for a distance of 20 km. It then turned back and returned to its starting point, having travelled a total of 7 hours. On its return trip, at a distance of 12 km from the starting point it encountered a log which had passed the starting point at the moment at which the boat had started downstream. The downstream speed of the boat is

Let the downstream speed be B and the upstream speed be U, and since the total time is 7 hours, 20/B plus 20/U equals 7. The log travels at the speed of the current, so the time it takes to reach the point 12 km from the start equals the total time the boat is on the river, giving 12 divided by the current speed equals 7. Using these two equations to relate the distances, the upstream speed U is equal to 1.5 times the current speed, leading to the proportional difference 20/B = 7 minus 20/U, which yields a downstream speed of 10 km/h.

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