A man can row at the rate of 3.5 , km/h in st | vedclass

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(B) Let the speed of the man in still water be $x = 3.5 \, km/h$ and the speed of the current be $y \, km/h$.The speed upstream is $(x - y) \, km/h$ a

Vedclass · Accepted Answer

$1.5$

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(B) Let the speed of the man in still water be $x = 3.5 \, km/h$ and the speed of the current be $y \, km/h$.The speed upstream is $(x - y) \, km/h$ and the speed downstream is $(x + y) \, km/h$.Let the distance be $d$. The time taken to row upstream is $T_u = \frac{d}{x - y}$ and the time taken to row downstream is $T_d = \frac{d}{x + y}$.According to the problem,$T_u = 2.5 	imes T_d$,which is $\frac{d}{x - y} = \frac{5}{2} 	imes \frac{d}{x + y}$.Canceling $d$ from both sides,we get $\frac{1}{x - y} = \frac{5}{2(x + y)}$,which implies $2(x + y) = 5(x - y)$.Expanding the equation: $2x + 2y = 5x - 5y$.Rearranging the terms: $7y = 3x$.Substituting $x = 3.5$: $7y = 3 	imes 3.5 = 10.5$.Therefore,$y = \frac{10.5}{7} = 1.5 \, km/h$.

$A$ man can row at the rate of $3.5 \, km/h$ in still water. If the time taken to row a certain distance upstream is $2 \frac{1}{2}$ times as much as the time taken to row the same distance downstream,find the speed of the current in $km/h$.

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