The speed of a motorboat in still water is 9, | vedclass

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Question

(D) Let the speed of the current be $x\,km/h$.Speed downstream = $(9 + x)\,km/h$.Speed upstream = $(9 - x)\,km/h$.Time taken downstream = $\frac{12}{9

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) Let the speed of the current be $x\,km/h$.Speed downstream = $(9 + x)\,km/h$.Speed upstream = $(9 - x)\,km/h$.Time taken downstream = $\frac{12}{9 + x}$.Time taken upstream = $\frac{12}{9 - x}$.Total time = $3\,hours$,so $\frac{12}{9 + x} + \frac{12}{9 - x} = 3$.Dividing by $3$: $\frac{4}{9 + x} + \frac{4}{9 - x} = 1$.$4(9 - x) + 4(9 + x) = (9 + x)(9 - x)$.$36 - 4x + 36 + 4x = 81 - x^2$.$72 = 81 - x^2$.$x^2 = 81 - 72 = 9$.$x = 3\,km/h$ (since speed cannot be negative).

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