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

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) (Show Source): You can put this solution on YOUR website!
.


Officials drain the lake at the rate of    of its volume per week.


The river fills the lake at the rate of    of its volume per week.


The net draining rate is   =  =   of the volume per week.


Hence, it will take   = 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
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    - Solving more complicated word problems on joint work
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Also, you have this free of charge online textbook in ALGEBRA-I in this site
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The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

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

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