A motorboat takes 18 hours to go downstream, and it takes 36 hours to return the same distance. Find the ratio of the speed of the boat in still water to the speed of the stream.

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Accepted Answer

Let the distance be D, speed of boat in still water be b, and speed of stream be s.

Downstream speed = b + s
Upstream speed = b - s

Time downstream = 18 hours, Time upstream = 36 hours

Using speed = distance/time,
D = (b + s) * 18  ...(1)
D = (b - s) * 36  ...(2)

From (1) and (2),
(b + s) * 18 = (b - s) * 36

Divide both sides by 18:
(b + s) = 2(b - s)

b + s = 2b - 2s

Bring terms to one side:
2b - b = s + 2s
b = 3s

Therefore, the ratio of speed of boat in still water to speed of stream is b : s = 3 : 1.

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