SOLUTION: pipe A can fill an empty water tank in 3hours, while pipe B can fill the same tank in 6 hours. when the tank is full it can be emptied by pipe C in 8 hours. pipes A and B are open

Algebra ->  Rate-of-work-word-problems -> SOLUTION: pipe A can fill an empty water tank in 3hours, while pipe B can fill the same tank in 6 hours. when the tank is full it can be emptied by pipe C in 8 hours. pipes A and B are open      Log On


   

Question 1149841: pipe A can fill an empty water tank in 3hours, while pipe B can fill the same tank in 6 hours. when the tank is full it can be emptied by pipe C in 8 hours. pipes A and B are opened at the same time when the tank is empty. if one hour later , pipe C is opened. find the total time taken to fill the tank?
Answer by ikleyn(52770) About Me  (Show Source):
You can put this solution on YOUR website!
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The combined rate of the pipes A and B is filling  1%2F3 + 1%2F6 = 3%2F6 = 1%2F2  of the tank volume per hour.


So, after 1 hour working, the two pipes A and B will fill  1%2F2  of the tank volume.



The combined net inflow rate of the three pipes A, B and C  is  1%2F3 + 1%2F6 - 1%2F8 = 8%2F24+%2B+4%2F24+-+3%2F24 = 9%2F24 = 3%2F8 of the tank volume per hour.


Hence, the three pipes will fill the remaining  1%2F2  of the tank volume in  %28%281%2F2%29%29%2F%28%283%2F8%29%29 = 8%2F6 hours = 12%2F6 hours = 

= 11%2F3 hours = 1 hour and 20 minutes.


The total time to fill the tank is then  2 hours and 20 minutes.    ANSWER

Solved.