SOLUTION: A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. Ho

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. Ho      Log On


   

Question 900943: A pipe can fill a tank in 3 hours if the drain is open. If the pipe runs with the drain open for 1 hour and the drain is then closed, the tank will be filled in 40 minutes more. How long does it take the pipe to fill the tank if the drain is closed?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Recognize, this is a uniform rates situation following RT=J for rate, time, Number_of_Tanks_to_Fill.

The fill pipe rate is 1/x.
The drain pipe FILL rate is -1/y.
Combined pipes fill rate is 1/3.
Also, combined pipes fill rate is 1%2Fx-1%2Fy=1%2F3.

Run the pipes both for 1 hour and then just the fill pipe for 2%2F3 hour. That fills the tank, 1 tank.

highlight%28%281%2F3%29%2A1%2B%281%2Fx%29%282%2F3%29=1%29-----Note very carefully, x is the time for the "pipe" to fill the tank if the drain is NOT in operation.
Solve for x. Unit is hours.