A boat travels 2, km upstream in a stream flo | vedclass

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(B) Let the speed of the boat in still water be $x\, km/h$ and the speed of the stream be $y = 3\, km/h$.The speed upstream is $(x - 3)\, km/h$ and th

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$9$

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(B) Let the speed of the boat in still water be $x\, km/h$ and the speed of the stream be $y = 3\, km/h$.The speed upstream is $(x - 3)\, km/h$ and the speed downstream is $(x + 3)\, km/h$.The total time taken is $30\, minutes = 0.5\, hours$.The time taken for the round trip is given by: $\frac{d}{x-y} + \frac{d}{x+y} = t$.Substituting the values: $\frac{2}{x-3} + \frac{2}{x+3} = 0.5$.$\frac{2(x+3) + 2(x-3)}{(x-3)(x+3)} = 0.5$.$\frac{2x + 6 + 2x - 6}{x^2 - 9} = 0.5$.$\frac{4x}{x^2 - 9} = 0.5$.$4x = 0.5(x^2 - 9) \Rightarrow 8x = x^2 - 9$.$x^2 - 8x - 9 = 0$.$(x - 9)(x + 1) = 0$.Since speed cannot be negative,$x = 9\, km/h$.

$A$ boat travels $2\, km$ upstream in a stream flowing at $3\, km/h$ and then returns downstream to the starting point in $30\, minutes$. The speed of the boat in still water is........$km/h$.

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