# Math

Two pumps are filling a pool. One of them is high power and can fill the pool alone in 2 hours less time than the other can do so. Given that, working together, both pumps can fill the pool in 144 minutes, how long, in hours, will it take the powerful pump to fill the pool alone?

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1. 1/x + 1/(x-2) = 60/144
now just solve for x

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2. s = smaller pump fill time ; b = bigger pump fill time

s = b + 120

(144 / s) + (144 / b) = 1

[144 / (b + 120)] + (144 / b) = 1

144 b + 144 b + (144 * 120) = b (b + 120)

0 = b^2 - 168 b - 17280

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3. The answer is 4 hours

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