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Question
A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
Solution
Let the speed of the stream be s km/h.
Speed of the motor boat 24 km / h
Speed of the motor boat upstream 24 s
Speed of the motor boat downstream 24 s
According to the given condition
`32/(24-s)-32/(24+s)=1`
∴ `32(1/(24-s)-1/(24+s))=1`
∴ `32((24+s-24+s)/(576-s^2))=1`
∴ 32 x 2s = 576 - s2
∴ s2 + 64s-576 = 0
∴ (s+72)(s-8) = 0
∴ s = -72 or s = 8
Since, speed of the stream cannot be negative, the speed of the stream is 8 km / h.
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