SOLUTION: Two taps can fill a tank in 12 minutes and 15 minutes respectively. Third tap can empty the tank in 6 minutes. Both the taps are opened and after 5 minutes third tap is also opened

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Question 1117234: Two taps can fill a tank in 12 minutes and 15 minutes respectively. Third tap can empty the tank in 6 minutes. Both the taps are opened and after 5 minutes third tap is also opened. In how many minutes will the tank be emptied ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two taps can fill a tank in 12 minutes and 15 minutes respectively.
Third tap can empty the tank in 6 minutes.
Both the taps are opened and after 5 minutes third tap is also opened.
In how many minutes will the tank be emptied ?
:
let t = time to empty the tank with 3rd tap
then
(t+5) = total time the 1st and 2nd taps are on
:
%28t%2B5%29%2F12 + %28t%2B5%29%2F15 = t%2F6
multiply equation by 60
60*%28t%2B5%29%2F12 + 60*%28t%2B5%29%2F15 = 60*t%2F6
cancel the denominators
5(t+5) + 4(t+5) = 10t
5t + 25 + 4t + 20 = 10t
9t + 45 = 10t
45 = 10t - 9t
t = 45 min for the tank to empty