SOLUTION: A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty

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Question 972456: A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty and all three pipes are open, in how many hours will the tank be filled?
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
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 draining for the 3 pipes to get
the rate of filling with all 3 open
----------------------------
rates of filling:
[ 1 tank filled ] / [ 4 hrs ]
[ 1 tank filled ] / [ 6 hrs ]
rate of draining:
[ 1 tank drained ] / [ 3 hrs ]
--------------------------
Let +t+ = time in hrs for the tank to be
filled with all 3 pipes open
+1%2F4+%2B+1%2F6+=+1%2F3+=+1%2Ft+
Multiply both sides by +12t+
+3t+%2B+2t+-+4t+=+12+
+t+=+12+
In 12 hrs, the tank will be filled with
all 3 pipes open
--------------------
check:
+.25+%2B+.1667+-+.333+=+.08333+
+.0834+=+.0833+
OK -error due to rounding off