A river has a steady speed of v. A man swims | vedclass

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(D) The total distance to be covered is $2d$ (distance $d$ upstream and $d$ downstream).In still water, the man swims at speed $2v$. The time taken to

Vedclass · Accepted Answer

$\frac{4}{3}$

Vedclass · Answer

(D) The total distance to be covered is $2d$ (distance $d$ upstream and $d$ downstream).In still water, the man swims at speed $2v$. The time taken to cover distance $2d$ is $t_0 = \frac{2d}{2v} = \frac{d}{v}$.When swimming downstream, the effective speed is $v_{down} = v_m + v_r = 2v + v = 3v$. The time taken is $t_1 = \frac{d}{3v}$.When swimming upstream, the effective speed is $v_{up} = v_m - v_r = 2v - v = v$. The time taken is $t_2 = \frac{d}{v}$.The total time taken is $t = t_1 + t_2 = \frac{d}{3v} + \frac{d}{v} = \frac{d + 3d}{3v} = \frac{4d}{3v}$.Therefore, the ratio is $\frac{t}{t_0} = \frac{4d/3v}{d/v} = \frac{4}{3}$.

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