SOLUTION: An inlet pipe on a swimming pool can be used to fill the pool in 36 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 12 filled and then the inlet pip

Algebra ->  Rate-of-work-word-problems -> SOLUTION: An inlet pipe on a swimming pool can be used to fill the pool in 36 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 12 filled and then the inlet pip      Log On


   

Question 923721: An inlet pipe on a swimming pool can be used to fill the pool in 36 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 12 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Does " 12 filled " mean " 1/2 filled" ?
I'll bet it does
If so,
The rate of filling is:
( 1 pool filled ) / ( 36 hrs )
The rate of draining is:
( 1 pool drained ) / ( 45 hrs )
---------------------------
Add the rates to get their rates together
Make the draining rate negative, though
Let +t+ = time in hrs to fill 1/2 of the pool
+1%2F36+-+1%2F45+=+%281%2F2%29+%2F+t+
+1%2F36+-+1%2F45+=+1%2F%282t%29+
Multiply both sides by +2%2A36%2A45t+
+90t+-+72t+=+36%2A45+
+18t+=+1620+
+t+=+90+
It will take 90 hrs to fill the pool
check:
+1%2F36+-+1%2F45+=+1%2F%282%2A90%29+
+1%2F36+-+1%2F45+=+1%2F180+
+5%2F180+-+4%2F180+=+1%2F180+
+1%2F180+=+1%2F180+
OK