SOLUTION: A pool can be filled in 96 hours and drained in 144 hours. How many hours will it take to fill the pool if both the fill and drain pipes are on

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Question 1155701: A pool can be filled in 96 hours and drained in 144 hours. How many hours will it take to fill the pool if both the fill and drain pipes are on
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52906) About Me  (Show Source):
You can put this solution on YOUR website!
.

The rate of filling is  1%2F96  of the tank volume per hour.


The rate of draining is  1%2F144  of the tank volume per hour.


The net inflow rate is  1%2F96 - 1%2F144 = %281%2F24%29%2A%281%2F3+-+1%2F4%29 = %281%2F24%29%2A%284%2F12-3%2F12%29 = %281%2F24%29%2A%281%2F12%29  of the tank volume per hour.


It means that the tank will be filled in  24*12 = 288 hours, if both filling and draining pipes are turned on.

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.


Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative to the method shown by tutor @ikleyn for solving problems like this. For this particular problem, it makes the solution almost trivial.

Consider the least common multiple of the two given times -- 96 hours and 144 hours. The least common multiple of those two times is 288 hours.

In 288 hours, the pool could be filled 288/96 = 3 times and it could be drained 288/144 = 2 times.

So in 288 hours with both the fill and drain pipes open the pool could be filled 3-2=1 time.

ANSWER: It takes 288 hours for the pool to fill if both pipes are open.