In a stream running at 2 , km/h,a motorboat g | vedclass

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Question

(C) Let the speed of the motorboat in still water be $x \, km/h$.The speed upstream is $(x - 2) \, km/h$ and the speed downstream is $(x + 2) \, km/h$

Vedclass · Accepted Answer

$22$

Vedclass · Answer

(C) Let the speed of the motorboat in still water be $x \, km/h$.The speed upstream is $(x - 2) \, km/h$ and the speed downstream is $(x + 2) \, km/h$.The total time taken is $55 \, min = \frac{55}{60} \, hours = \frac{11}{12} \, hours$.According to the problem:$\frac{10}{x - 2} + \frac{10}{x + 2} = \frac{11}{12}$$10 \left( \frac{x + 2 + x - 2}{x^2 - 4} ight) = \frac{11}{12}$$10 \left( \frac{2x}{x^2 - 4} ight) = \frac{11}{12}$$20x 	imes 12 = 11(x^2 - 4)$$240x = 11x^2 - 44$$11x^2 - 240x - 44 = 0$$11x^2 - 242x + 2x - 44 = 0$$11x(x - 22) + 2(x - 22) = 0$$(11x + 2)(x - 22) = 0$Since speed cannot be negative,$x = 22 \, km/h$.

In a stream running at $2 \, km/h$,a motorboat goes $10 \, km$ upstream and returns to the starting point in $55 \, min$. Find the speed of the motorboat in still water (in $km/h$).

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