SOLUTION: Two inlet pipes can fill a water reservoir in 10 hours and 12 hours respectively when opened individually. If an outlet can empty the reservoir alone in 9 hours, how long will it t

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Question 724060: Two inlet pipes can fill a water reservoir in 10 hours and 12 hours respectively when opened individually. If an outlet can empty the reservoir alone in 9 hours, how long will it take to fill the reservoir if all 3 pipes are opened simultaneously?
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of filling and subtract the
rate of emptying to get the rate of filling
with all 3 pipes open.
( 1 reservoir filled ) / ( 10 hrs ) + ( 1 reservoir filled ) / ( 12 hrs ) - ( 1 reservoir emptied ) / ( 9 hrs )
= ( 1 reservoir filled / t hrs )
--------------------------
+1%2F10+%2B+1%2F12+-+1%2F9+=+1%2Ft+
I'll multiply both sides by +360t+
+36t+%2B+30t+-+40t+=+360+
+26t+=+360+
+t+=+13.846+ hrs
+.846%2A60+=+50.8+
It will take 13 hrs and 51 min to fill the reservoir
That's it unless there's a math error
check:
+.1+%2B+.08333+-+.1111+=+1%2Ft+
+.0722223+=+1%2Ft+
+t+=+13.846+
OK