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

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(A) Let the speed of the motorboat in still water be $x \ km/h$.Given the speed of the stream $y = 2 \ km/h$.The speed upstream is $(x - 2) \ km/h$ an

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$22$

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(A) Let the speed of the motorboat in still water be $x \ km/h$.Given the speed of the stream $y = 2 \ km/h$.The speed upstream is $(x - 2) \ km/h$ and the speed downstream is $(x + 2) \ km/h$.The total time taken is $33 \ minutes = \frac{33}{60} \ hours = \frac{11}{20} \ hours$.According to the problem: $\frac{6}{x-2} + \frac{6}{x+2} = \frac{11}{20}$.$6 \left( \frac{x+2+x-2}{x^2-4} ight) = \frac{11}{20} \Rightarrow 6 \left( \frac{2x}{x^2-4} ight) = \frac{11}{20}$.$12x 	imes 20 = 11(x^2 - 4) \Rightarrow 240x = 11x^2 - 44$.$11x^2 - 240x - 44 = 0$.$11x^2 - 242x + 2x - 44 = 0 \Rightarrow 11x(x - 22) + 2(x - 22) = 0$.$(x - 22)(11x + 2) = 0$.Since speed cannot be negative,$x = 22 \ km/h$.

In a stream running at $2 \ km/h$,a motorboat goes $6 \ km$ upstream and back again to the starting point in $33 \ minutes$. Find the speed of the motorboat in still water. (in $km/h$)

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