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Let the speed of a boat in still water be uu km/hr and the speed of the water current in a river be vv km/hr. If a man rows distance DD down stream and same distance upstream, then average speed of total journey is

Solution

✅ Correct Option: 2

Average speed is total distance divided by total time:

2DDu+v+Du−v\dfrac{2D}{\dfrac{D}{u+v}+\dfrac{D}{u-v}}.

The denominator simplifies to 2Du(u+v)(u−v)\dfrac{2Du}{(u+v)(u-v)}.

Hence the average speed is (u+v)(u−v)u\dfrac{(u+v)(u-v)}{u}, the harmonic mean of the two speeds.

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