SOLUTION: Pump R can fill a tank in 8 hours and Pump Q can empty it in 12 hours. If both pumps are in operation, how long will it take to fill the tank?

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Question 1163866: Pump R can fill a tank in 8 hours and Pump Q can
empty it in 12 hours. If both pumps are in operation,
how long will it take to fill the tank?

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

Pump R adds  1%2F8  of the tank volume per hour, 

while Pump Q  drains  1%2F12  of the tank volume per hour.


The net inflow rate is then the difference


    1%2F8 - 1%2F12 = 3%2F24+-+2%2F24 = 1%2F24  of the tank volume per hour.


Hence, in 24 hours the tank will be filled.

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.