SOLUTION: Hi, here's my question: A certain tank has an inlet valve and an outlet valve. The tank can be filled via the inlet valve in 6 minutes and emptied (from full) via the outlet val

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Hi, here's my question: A certain tank has an inlet valve and an outlet valve. The tank can be filled via the inlet valve in 6 minutes and emptied (from full) via the outlet val      Log On


   

Question 997058: Hi, here's my question:
A certain tank has an inlet valve and an outlet valve. The tank can be filled via the inlet valve in 6 minutes and emptied (from full) via the outlet valve in 10 minutes. If both valves are operating, how long would it take to fill the tank if it was empty to begin with?
Thanks!
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
Inlet increases the volume of the liquid in the tank in  1%2F6  of its capacity each minute.

The outlet decreases the volume of the liquid in the tank in  1%2F10  of its capacity each minute.

The balance is  1%2F6 - 1%2F10 = 5%2F30 - 3%2F30 = %285-3%29%2F30 = 2%2F30 = 1%2F15.

Thus the volume of the liquid in the tank increases in  1%2F15  of its capacity each minute.

Hence, it will take  15  minutes to fill the tank with the opened inlet and outlet.

For more similar problems see the lesson  Using fractions to solve word problems on joint work  in this site.