SOLUTION: A pipe can fill a pool in 9 hours and another pipe can empty the pool in 12 hours. If both pipes are left open at the same time, how long will it take to fill the pool?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A pipe can fill a pool in 9 hours and another pipe can empty the pool in 12 hours. If both pipes are left open at the same time, how long will it take to fill the pool?      Log On


   

Question 690250: A pipe can fill a pool in 9 hours and another pipe can empty the pool in 12 hours. If both pipes are left open at the same time, how long will it take to fill the pool?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
One pipe has a positive rate ( filling )
The other pipe has a negative rate ( emptying )
The 1st pipe's rate is ( 1 pool filled ) / ( 9 hrs )
The 2nd pipe's rate is ( 1 pool emptied ) / ( 12 hrs )
Let t = the time in hrs to fill the pool with both pipes open
Add their rates to get their rate working against each other
+1%2F9+-+1%2F12+=+1%2Ft+
Multiply both sides by +36+
+36%2F9+-+36%2F12+=+36%2Ft+
+4+-+3+=+36%2Ft+
+36%2Ft+=+1+
+t+=+36+
With both pipes open, the pool is filled in 36 hrs