SOLUTION: A swimming pool has two inlet pipes. One fills the pool in three hours and the other in 6 hours. The outlet pipe empties the pool in 4 hours. Once the outlet pipe was left open w

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A swimming pool has two inlet pipes. One fills the pool in three hours and the other in 6 hours. The outlet pipe empties the pool in 4 hours. Once the outlet pipe was left open w      Log On


   

Question 746611: A swimming pool has two inlet pipes. One fills the pool in three hours and the other in 6 hours. The outlet pipe empties the pool in 4 hours. Once the outlet pipe was left open when the pool was being filled, in how many hours was the pool full?
Please help. I am trying to help my son with his homework.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add the rates of filling of the 2 filling pipes and
subtract the rate of draining of the emptying pipe
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1st pipe's rate: ( 1 pool filled ) / ( 3 hrs )
2nd pipe's rate: ( 1 pool filled ) / ( 6 hrs )
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3rd pipe's rate of emptying: ( 1 pool emptied ) / ( 4 hrs )
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Let +t+ = the time in hrs to fill the pool with all 3 pipes open
+1%2F3+%2B+1%2F6+-1%2F4+=+1%2Ft+
Multiply both sides by +24t+
+8t+%2B+4t+-+6t+=+24+
+6t+=+24+
+t+=+4+
It will take 4 hrs to fill the pool with all 3 pipes open
check:
+1%2F3+%2B+1%2F6+-1%2F4+=+1%2Ft+
+1%2F3+%2B+1%2F6+-1%2F4+=+1%2F4+
Add +1%2F4+ to both sides
+1%2F3+%2B+1%2F6+=+1%2F2+
+2%2F6+%2B+1%2F6+=+1%2F2+
+3%2F6+=+1%2F2+
+1%2F2+=+1%2F2+
OK