SOLUTION: One hose can fill a pool in 8 hours, another hose can fill the pool in 6hrs. If both hoses are turned on, and a drain that can empty the pool in 24 is left open, can the pool ever

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Question 1156127: One hose can fill a pool in 8 hours, another hose can fill the pool in 6hrs. If both hoses are turned on, and a drain that can empty the pool in 24 is left open, can the pool ever get filled? If so, how long would it take?
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.

One hose fills    of the tank volume per hour.


Another hose fills    of the tank volume per hour.


Working together, these hoses fill   =  =   of the tank volume per hour.


The draining pipe takes off  of the tank volume per hour.


You see that inflow rate of two hoses is greater than the outflow rate of the draining pipe.


Therefore, the net inflow rate is positive; so tank will be steadily filled.



    Notice that even each single hose brings more water that the draining pipe takes off,
    so there is no ANY doubts that the tank will be filled - it is out of the question.



Now, the precise net inflow rate is   =  =   of the tank volume per hour.


So, the tank will be filled in 4 hours, if both hoses and draining pipe are turned on.

Solved.

----------------

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.


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