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.

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#### 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 - s^{2}

∴ s^{2} + 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.

Concept: Pair of Linear Equations in Two Variables

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