SOLUTION: Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe

Question 1117269: Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe is in use when both taps are turned on?
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
A joint-work problem. Some tutors have lessons here covering how to solve this type of problem. You should investigate and learn from them if you want to master it.

The approach is to see how much of the tank fills in a unit of time. A good choice for the unit of time is one minute, because the fill and empty times are given in minutes. We of course assume the tank is empty at the start.

A fills 1/6 of the tank per minute.
B fills 1/9 of the tank per minute.
C "fills" -1/15 of the tank per minute. Here the minus sign indicates it is actually emptying the tank.

Fill rate = tanks per minute
The time needed to fill one tank is therefore or about minutes (4 min, 44.2 sec).

Check: This is more of a qualitative check. Does our answer make sense?
Say the pipe emptying the tank was turned off. The two taps would fill the tank at a rate (1/6)+(1/9) = 5/18 tank/min. This corresponds to a fill time of 18/5 = 3.6 minutes. In the problem scenario the pipe is emptying the tank at 1/15 tank/min which is comparatively slower than the fill rate, so we'd expect the fill time to be extended, but only moderately. Our answer of 4.7368 minutes is moderately longer than 3.6 minutes so at least the answer seems about right.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
I want to thank the tutor @math_helper for mentioning that lessons on joint work.

The introductory lessons on this subject are
    - 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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