SOLUTION: Hello Tutors! I would be elated if someone can help me break down and solve this math riddle. It is worth points (and I am in desperate need). Thank you in advance for your time

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Question 1137731: Hello Tutors! I would be elated if someone can help me break down and solve this math riddle. It is worth points (and I am in desperate need). Thank you in advance for your time and patience. I struggle terribly with algebra.
Here it is:
If a vat of acid can be filled by an inlet pipe in 10 hr and emptied by an outlet pipe in 20 hr, how long will it take to fill the vat if both pipes are open? Assume that the vat is empty at the start.
Hint: This is essentially a variation of a distance - rate - time problem.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Fill Rate of Inlet,
Fill Rate of Outlet,
(Outlet drains the vat; it does not fill the vat.)

Both Pipes at the same time:








20 hours to fill, both pipes open
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
The inlet pipe fills and adds    of the vat volume per hour.


The outlet pipe drains and removes    of the vat volume per hour.


Therefore, the net inflow rate to the vat is   -  =  =   of the vat volume per hour.


It means that the vat will be filled in 20 hours, if both pipes work simultaneously.

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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