SOLUTION: To fill a swimming pool requires 2 hours if water enters through an inlet pipe alone, or 5 hours if water enters through a hose alone. An outlet pipe can drain the pool in 9 hours.

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Question 680819: To fill a swimming pool requires 2 hours if water enters through an inlet pipe alone, or 5 hours if water enters through a hose alone. An outlet pipe can drain the pool in 9 hours. If the inlet pipe, hose, and outlet pipe are all being used simultaneously, 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!
Add their rates of filling ( or emptying )
to get their rate when used together
( 1 pool filled / 2 hrs ) + ( 1 pool filled / 5 hrs ) + (1 pool ( filled or emptied )
= ( 1 pool filled / t hrs )
+1%2F2+%2B+1%2F5+%2B+1%2F9+=+1%2Ft+
Multiply both sides by +90t+
+45t+%2B+18t+%2B+10t+=+90+
+73t+=+90+
+t+=+1.233+ hrs
+.233%2A60+=+14+
It will take 1 hr and 14 min
check:
+.5+%2B+.2+%2B+.111+=+1%2Ft+
+.8111+=+1%2Ft+
+t+=+1.233+
OK