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 25 weeks in replenishing the lake

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Question 1174937: 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 25 weeks in replenishing the lake at the same time. How many weeks does it take to empty the lake
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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Officials drain the lake at the rate of  1%2F16  of its volume per week.


The river fills the lake at the rate of  1%2F25  of its volume per week.


The net draining rate is  1%2F16+-+1%2F25 = 25%2F400+-+16%2F400 = 9%2F400  of the volume per week.


Hence, it will take  400%2F9 = 44.44... weeks to empty the lake.    ANSWER

Solved.

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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.