SOLUTION: One pipe can fill a tank in 6 hours and another pipe can fill the same tank in 3 hours. A drain pipe can empty the tank in 24 hours. With all the pipes open, how long will it take

Question 944770: One pipe can fill a tank in 6 hours and another pipe can fill the same tank in 3 hours. A drain pipe can empty the tank in 24 hours. With all the pipes open, how long will it take to fill the tank?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
Pipe A fills 1 tank in 6 hours=1 tank/6 hrs=1/6 tank/hr
Pipe B fills 1 tank in 3 hours=1 tank/3 hrs=1/3 tank/hr
Since the drain empties the tank, it has a negative fill rate.
Pipe C (drain) empties -1 tank in 24 hours=-1 tank/24 hrs=-1/24 tank/hr
With all pipes open, the combined rate is:
Rate=A+B+C=1/6 tank/hr + 1/3 tank/hr + (-1/24 tank/ hr) Find common denominator
Rate=(1/6)(4/4) tank/hr+(1/3)(8/8) tank/hr +(-1/24) tank/hr
Rate=tank/hr
Rate=11/24 tank/hr With all pipes open, the tank fills at a rate of 11/24 tank/hr
To fill the whole tank: 1 tank/(11/24 tank/hr)=2.18 hours
ANSWER With all pipes open, the tank will fill in 2.18 hours.

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