# A motorboat whose

Let the speed of the stream be x km/h.

Speed of a 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 is taken by boat to go 32 km upstream,

Time is taken by boat to return 32 km downstream,

Given that,

t1 = t2 + 1

⇒

⇒

⇒ 32(24 + x) - 32(24 - x) = (24 + x)(24 - x)
⇒ 32(24) + 32x - 32(24) + 32x = 242 - x2

⇒ 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)

The speed of the stream is 8 km/h.

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