SOLUTION: A large pipe can empty the pool in 6 hours and a small pipe can empty the same pool in 9 hours.How long will it take for both pipes to empty the pool?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A large pipe can empty the pool in 6 hours and a small pipe can empty the same pool in 9 hours.How long will it take for both pipes to empty the pool?      Log On


   

Question 1042552: A large pipe can empty the pool in 6 hours and a small pipe can empty the same pool in 9 hours.How long will it take for both pipes to empty the pool?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Rate of emptying for large pipe:
[ 1 pool emptied ] / [ 6 hrs ]
Rate of emptying for small pipe:
[ 1 pool emptied ] / [ 9 hrs ]
---------------------------
Add their rates of emptying to get
the rate with both pipes together
Let +t+ = time in hrs with both
pipes emptying together
---------------------------
+1%2F6+%2B+1%2F9+=+1%2Ft+
Multiply both sides by +18t+
+3t+%2B+2t+=+18+
+5t+=+18+
+t+=+3.6+
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Both pipes together will empty the pool in
3.6 hrs
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check:
+1%2F6+%2B+1%2F9+=+1%2F3.6+
+.1667+%2B+.1111+=+.2777+
+.2778+=+.2777+
Error due to rounding off
OK