The speed of a motorboat in still water is 25 | vedclass

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Question

(A) Let the speed of the current be $x 	ext{ km/hr}$.Given, speed of motorboat in still water = $25 	ext{ km/hr}$.Speed downstream = $(25 + x) 	ext

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(A) Let the speed of the current be $x 	ext{ km/hr}$.Given, speed of motorboat in still water = $25 	ext{ km/hr}$.Speed downstream = $(25 + x) 	ext{ km/hr}$.Speed upstream = $(25 - x) 	ext{ km/hr}$.Time taken to travel $60 	ext{ km}$ downstream = $\frac{60}{25 + x} 	ext{ hours}$.Time taken to travel $60 	ext{ km}$ upstream = $\frac{60}{25 - x} 	ext{ hours}$.Total time = $5 	ext{ hours}$.So, $\frac{60}{25 + x} + \frac{60}{25 - x} = 5$.Divide by $5$: $\frac{12}{25 + x} + \frac{12}{25 - x} = 1$.$12(25 - x + 25 + x) = (25 + x)(25 - x)$.$12(50) = 625 - x^2$.$600 = 625 - x^2$.$x^2 = 25$.$x = 5 	ext{ km/hr}$ (since speed cannot be negative).Thus, the speed of the current is $5 	ext{ km/hr}$.

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