SOLUTION: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 16 weeks, but a river that can fill the lake in 30 weeks is replenishing the lake

Question 946670: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 16 weeks, but a river that can fill the lake in 30 weeks is replenishing the lake at the same time. How long does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.
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 16 weeks, but a river that can fill the lake in 30 weeks is replenishing the lake at the same time. How long does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.
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empty rate = 1/16 job/week
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fill rate = 1/30 job/week
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Together rate = 1/x job/week
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rate - rate = together rate
1/16 - 1/30 = 1/x
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30x - 16x = 16*30
14x = 16*30
x = (8/7)30
x = 34.29 weeks (time to empty the lake)
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Cheers,
Stan H.
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