SOLUTION: A large water tank has two inlet pipes of different sizes, and one outlet pipe. With the outlet pipe closed, it takes 3 hours to fill the empty tank using the large inlet pipe only

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Question 772695: A large water tank has two inlet pipes of different sizes, and one outlet pipe. With the outlet pipe closed, it takes 3 hours to fill the empty tank using the large inlet pipe only. It takes 4 hours to fill the empty tank using the small inlet pipe only. When the tank is full, and the inlet pipes are closed, it takes the outlet pipe 8 hours to empty the tank. Assuming the tank is empty and all three pipes are opened, how long will it take to fill the tank, to the nearest minute?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add the rates of filling and subtract
the rate of emptying
-------------------
Large pipe's rate:
( 1 tank ) / ( 3 hrs )
Small pipe's rate:
( 1 tank ) ( 4 hrs )
Outlet pipe's rate:
( 1 tank ) / ( 8 hrs )
-----------------
Let +t+ = time in hrs to fill
tank with all 3 open
+1%2F3+%2B+1%2F4+-+1%2F8+=+1%2Ft+
Multiply both sides by +24t+
+8t+%2B+6t+-+3t+=+24+
+11t+=+24+
+t+=+24%2F11+
+2.1818+ hrs
+.1818%2A60+=+10.91+
It takes 2 hrs and 11 minutes to fill tank