The time taken by a boat to travel a certain distance downstream is half the time taken to cover the same distance upstream. If the boat covers 128 km downstream in t hours and 96 km upstream in (t + 2) hours, find the speed of the boat in still water (in km/hr).

Let the boat's speed in still water be b and the stream's speed be s; the downstream speed is b + s and the upstream speed is b - s. Since the downstream time is half the upstream time for the same distance, the downstream speed is twice the upstream speed: b + s = 2(b - s), which simplifies to b = 3s. The downstream speed is 128/t and the upstream speed is 96/(t + 2); equating the ratio gives 128(t + 2) = 2(96t), which solves to t = 4 hours. Substituting t back gives a downstream speed of 32 km/hr and upstream speed of 16 km/hr, meaning the boat's speed in still water is (32 + 16)/2 = 24 km/hr.

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