A motorboat travelling at some speed can cover 24 km upstream and 40 km downstream in 17 hours. At the same speed it can travel 32 km downstream and 12 km upstream in 10 hours. Find the speed of the stream.

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Let the speed of the boat in still water be 'b' km/h and the speed of the stream be 's' km/h.

Upstream speed = (b - s) km/h
Downstream speed = (b + s) km/h

From the first condition:
Time taken upstream + Time taken downstream = 17 hours
=> 24 / (b - s) + 40 / (b + s) = 17  ...(1)

From the second condition:
32 / (b + s) + 12 / (b - s) = 10  ...(2)

Multiply equation (1) by (b - s)(b + s) to clear denominators:
24(b + s) + 40(b - s) = 17(b^2 - s^2)
=> 24b + 24s + 40b - 40s = 17(b^2 - s^2)
=> 64b - 16s = 17(b^2 - s^2)  ...(3)

Multiply equation (2) similarly:
32(b - s) + 12(b + s) = 10(b^2 - s^2)
=> 32b - 32s + 12b + 12s = 10(b^2 - s^2)
=> 44b - 20s = 10(b^2 - s^2)  ...(4)

Let x = b^2 - s^2
From (3): 64b - 16s = 17x
From (4): 44b - 20s = 10x

Multiply (4) by 1.7 to align with (3):
44b*1.7 - 20s*1.7 = 10x*1.7
=> 74.8b - 34s = 17x

Subtract (3) from this:
(74.8b - 64b) - (34s - (-16s)) = 17x - 17x
=> 10.8b - 18s = 0
=> 10.8b = 18s
=> b = (18/10.8)s = (5/3)s

Substitute b = (5/3)s into (3):
64*(5/3)s - 16s = 17((5/3)^2 s^2 - s^2)
=> (320/3)s - 16s = 17((25/9)s^2 - s^2)
=> (320/3)s - 16s = 17((25/9 - 9/9)s^2)
=> (320/3)s - 16s = 17((16/9)s^2)
=> (320/3)s - 16s = (272/9)s^2

Convert left side to common denominator 3:
(320/3)s - (48/3)s = (272/9)s^2
=> (272/3)s = (272/9)s^2

Divide both sides by s (s ≠ 0):
(272/3) = (272/9)s

Multiply both sides by 9:
272 * 3 = 272 * s

Divide both sides by 272:
3 = s

Therefore, the speed of the stream is 3 km/h.

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