SOLUTION: A certain tank has an inlet valve and an outlet valve. The tank can be filled via the inlet valve in 6 mins and empties via the outlet in 10 mins. If both valves are operating, how

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A certain tank has an inlet valve and an outlet valve. The tank can be filled via the inlet valve in 6 mins and empties via the outlet in 10 mins. If both valves are operating, how      Log On


   

Question 1110677: A certain tank has an inlet valve and an outlet valve. The tank can be filled via the inlet valve in 6 mins and empties via the outlet in 10 mins. If both valves are operating, how long would it take to fill the tank if it was empty to begin with?
Please explain it step by step, I usually struggle with rates.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The inlet adds  1%2F6 of the tank volume each minute.


The outlet removes  1%2F10  of the tank volume each minute.


The net is  PLUS  1%2F6 - 1%2F10 = 5%2F30 - 3%2F30 = 2%2F30 = 1%2F15  of the tank volume each minute.


Hence, it will take 15 minutes.

Solved.

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It is a 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.