SOLUTION: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 6 weeks, but a river that can fill the lake in 15 weeks is replenishing the la

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Question 989360: Officials begin to release water from a full man-made lake at a rate that would empty the lake in
6 weeks, but a river that can fill the lake in
15 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 solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The drain empties the full lake in six weeks, so in one week the drain empties th of the lake. Likewise, in one week, the fill replenishes of the lake. Working together, the lake drains at a rate of:



of the lake per week. Applying the LCD:



of the lake is emptied in one week, so it takes



weeks to empty the lake.

John

My calculator said it, I believe it, that settles it