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A swimmer crosses a flowing stream of width ‘d’ to and fro in time $t_{1} .$ The time taken to cover the same distance up and down the stream is $t_{2} .$ If $t_{3}$ is the time taken by swimmer if he would take to swim a distance 2d in still water then:

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$t_{3} = t_{1} + t_{2}$

$t_{3}^{2} = t_{1} t_{2}$

$t_{2}^{2} = t_{1} t_{3}$

$t_{1}^{2} = t_{2} t_{3}$

answer is D.

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Detailed Solution

$t_{1} = \frac{d}{\sqrt{v_{b r}^{2} - v_{r}^{2}}}; t_{2} = \frac{d}{v_{b r} + v_{r}} + \frac{d}{v_{b r} - v_{r}}; t_{3} = \frac{2 d}{v_{b r}}$

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