Question 590666: A tank has supply pipe A and an exhaust pipe B. The pipe A takes 4 minutes less to fill a tank than the pipe B takes to empty it. When both are open, the tank is filled in 24 minutes. Find the time needed for pipe A to fill the tank when pipe B is closed.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! A tank has supply pipe A and an exhaust pipe B. The pipe A takes 4 minutes less to fill a tank than the pipe B takes to empty it. When both are open, the tank is filled in 24 minutes. Find the time needed for pipe A to fill the tank when pipe B is closed.
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let x=minutes pipe B takes to empty tank
1/x=pipe B work rate
x-4=minutes pipe A takes to fill tank
1/(x-4)=Pipe A work rate
..
In 24 minutes:
24/(x-4)-24/x=100%
24x-24x+96=x(x-4)=x^2-4x
x^2-4x-96=0
(x-12)(x+8)=0
x=-8 (reject, x>0)
x=12
x-4=8
ans:
Pipe A alone fills tank in 8 minutes (When Pipe B is closed)
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