SOLUTION: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 18 weeks,but a river that can fill the lake in 25 weeks is replenishing the lake a

Question 509222: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 18 weeks,but a river that can fill the lake in 25 weeks is replenishing the lake at the same time. How long does it take to empty the lake?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Officials begin to release water from a full man-made lake at a rate that would empty the lake in 18 weeks,but a river that can fill the lake in 25 weeks is replenishing the lake at the same time. How long does it take to empty the lake?
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Empty rate = 1/18 job/week
---
Fill rate = 1/25 job/week
---
Together rate: 1/x
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Equation:
rate - rate = together rate
1/18 - 1/25 = 1/x
----
Multiply thru by 18*25x
---
25x - 18x = 18*25
7x = 18*25
x = 64.29 weeks (time required to empty)
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Cheers,
Stan H.

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