Q75 of 82 Page 4

A motor boat whose speed is 24 km/h in still water takes 1 hr more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream. (CBSE 2016)

Let the speed of stream be x km/h.


Speed of boat in still water is 24 km/h.


Speed of boat in upstream : (24 - x) km/h


Speed of boat in downstream : (24 + x) km/h


Time taken by boat to go 32 km upstream,


Time taken by boat to return 32 km downstream,


Given that,


t1 = t2 + 1


→


→


32(24 + x) - 32(24 - x) = (24 + x)(24 - x)


64x = 576 - x2


x2 + 64x - 576 = 0


x2 + 72x - 8x - 576 = 0


x(x + 72) - 8(x + 72) = 0


(x - 8)(x + 72) = 0


x = 8 or x = - 72 (not possible as speed cannot be negative)


Speed of stream is 8 km/h

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