A person,rowing at the rate of 5 , km/h in st | vedclass

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(C) Let the speed of the stream be $v \, km/h$.Given that,the speed of the person in still water is $5 \, km/h$.The speed of the person downstream is

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(C) Let the speed of the stream be $v \, km/h$.Given that,the speed of the person in still water is $5 \, km/h$.The speed of the person downstream is $(5 + v) \, km/h$.The speed of the person upstream is $(5 - v) \, km/h$.Time taken to cover $40 \, km$ downstream is $t_1 = \frac{40}{5 + v} \, h$.Time taken to cover $40 \, km$ upstream is $t_2 = \frac{40}{5 - v} \, h$.According to the problem,the time taken upstream is thrice the time taken downstream,so $t_2 = 3 	imes t_1$.Substituting the values: $\frac{40}{5 - v} = 3 	imes \frac{40}{5 + v}$.Dividing both sides by $40$: $\frac{1}{5 - v} = \frac{3}{5 + v}$.Cross-multiplying: $5 + v = 3(5 - v)$.$5 + v = 15 - 3v$.$4v = 10$.$v = 2.5 \, km/h$.Thus,the speed of the stream is $2.5 \, km/h$.

$A$ person,rowing at the rate of $5 \, km/h$ in still water,takes thrice as much time in going $40 \, km$ upstream as in going $40 \, km$ downstream. Find the speed of the stream in $km/h$.

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