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Q.

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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a

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

b

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

c

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

d

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

answer is A.

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Detailed Solution

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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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A swimmer crosses a flowing stream of width W to and fro in time t1. The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2W in still water, then