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(B) Let the total distance between the two points be $d\, km$.Speed of the boat in still water = $8\, km/h$.Speed of the stream = $2\, km/h$.Downstrea

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(B) Let the total distance between the two points be $d\, km$.Speed of the boat in still water = $8\, km/h$.Speed of the stream = $2\, km/h$.Downstream speed = $8 + 2 = 10\, km/h$.Usual time taken to cover distance $d$ downstream = $\frac{d}{10}$.In the actual scenario,the man travels half the distance $(d/2)$ at $10\, km/h$ and the remaining half $(d/2)$ at the speed of the stream $(2\, km/h)$ because the motor failed.Actual time taken = $\frac{d/2}{10} + \frac{d/2}{2} = \frac{d}{20} + \frac{d}{4} = \frac{d + 5d}{20} = \frac{6d}{20} = \frac{3d}{10}$.Given that the actual time is $6\, hours$ more than the usual time:$\frac{3d}{10} - \frac{d}{10} = 6$$\frac{2d}{10} = 6$$\frac{d}{5} = 6$$d = 30\, km$.

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