SOLUTION: Pipe A can fill a tank in 4 hours and pipe B can fill the tank in 1/2 the time required for pipe C to empty the tank. When all three pipes are open the tank is filled in 2.4 hours.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pipe A can fill a tank in 4 hours and pipe B can fill the tank in 1/2 the time required for pipe C to empty the tank. When all three pipes are open the tank is filled in 2.4 hours.      Log On


   

Question 920224: Pipe A can fill a tank in 4 hours and pipe B can fill the tank in 1/2 the time required for pipe C to empty the tank. When all three pipes are open the tank is filled in 2.4 hours. How long for C to drain the tank?
I tried setting up a table. But I'm not sure what the significance of whether the tank is being filled or emptied is.
Thank you for helping.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Rates of FILLING are (+)
Rates of emptying are (-)
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Rate of filling for pipe A:
( 1 tank ) / ( 4 hrs )
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Let +-R+ = rate of emptying for pipe C
+2R+ = rate of filling for pipe B
( 1/2 the time means twice the rate )
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Add the rates with all 3 pipes open:
+1%2F4+%2B+2R+-+R+=+1+%2F+2.4+
Multiply both sides by 2.4%2A4+
+2.4+%2B+19.2R+-+9.6R+=+4+
+9.6R+=+1.6+
+R+=+1%2F6+
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+-R+=+-1%2F6+
In minutes:
+-R+=+%28+-1%2F6+%29%2A60++
+-R+=+-10+
Pipe C drains the tank in 10 min
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check:
+1%2F4+%2B+2R+-+R+=+1+%2F+2.4+
+1%2F4+%2B+2%2A%281%2F6%29+-+1%2F6+=+1+%2F+2.4+
Multiply both sides by +12+
+3+%2B+4+-+2+=+5+
+5+=+5+
OK