SOLUTION: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 8 weeks, but a river that can fill the lake in 15 weeks is replenishing the lake a
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Question 1050064: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 8 weeks, but a river that can fill the lake in 15 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The rate of emptying the lake is:
[ 1 lake emptied ] / [ 8 wks ]
I will call emptying a negative rate, so
this rate is
-----------------------------------
The rate of filling the lake is:
[ 1 lake filled ] / [ 15 wks ]
This is a positive rate of
--------------------------------
Let = time in weeks to empty lake
Add the given rates to get a total
negative rate of emptying of
-------------------------------------
Multiply both sides by
it will take 17 weeks and 1 day to empty the lake
--------------------
check:
OK
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