A man takes 3 hours 45 minutes to row a boat | vedclass

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Question

(A) Let the speed of the boat in still water be $x \; km/hr$ and the speed of the river current be $y \; km/hr$.Downstream speed $= x + y$.Time taken

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(A) Let the speed of the boat in still water be $x \; km/hr$ and the speed of the river current be $y \; km/hr$.Downstream speed $= x + y$.Time taken downstream $= 3 \; hours \; 45 \; minutes = 3 + \frac{45}{60} = 3 + \frac{3}{4} = \frac{15}{4} \; hours$.Distance $= 15 \; km$.Using $	ext{Speed} = \frac{	ext{Distance}}{	ext{Time}}$,we get $x + y = \frac{15}{15/4} = 4 \; km/hr \; \dots (i)$.Upstream speed $= x - y$.Time taken upstream $= 2 \; hours \; 30 \; minutes = 2 + \frac{30}{60} = 2.5 = \frac{5}{2} \; hours$.Distance $= 5 \; km$.Using $	ext{Speed} = \frac{	ext{Distance}}{	ext{Time}}$,we get $x - y = \frac{5}{5/2} = 2 \; km/hr \; \dots (ii)$.Subtracting equation $(ii)$ from equation $(i)$:$(x + y) - (x - y) = 4 - 2$$2y = 2$$y = 1 \; km/hr$.Thus,the speed of the river current is $1 \; km/hr$.

$A$ man takes $3$ $hours$ $45$ $minutes$ to row a boat $15 \; km$ downstream of a river and $2$ $hours$ $30$ $minutes$ to cover a distance of $5 \; km$ upstream. Find the speed of the river current in $km/hr$.

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