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A swimmer crosses a flowing stream of width W 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 the swimmer would take to swim a distance 2W in still water, then

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

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

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

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

answer is A.

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Detailed Solution

Let v be the river velocity and u the velocity of swimmer in still water. Then

$t_{1} = 2 (\frac{W}{\sqrt{u^{2} - v^{2}}})$

$t_{2} = \frac{W}{u + v} + \frac{W}{u - v} = \frac{2 uW}{u^{2} - v^{2}} and t_{3} = \frac{2 W}{u}$

Now we can see that ${t_{1}}^{2} = t_{2} t_{3}$

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