SOLUTION: One pipe can fill a tank in 45 minutes and another pipe can fill it in 30 minutes. if these two pipes are open and a third pipe is draining water from the tank, it takes 27 minutes

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One pipe can fill a tank in 45 minutes and another pipe can fill it in 30 minutes. if these two pipes are open and a third pipe is draining water from the tank, it takes 27 minutes      Log On


   

Question 761369: One pipe can fill a tank in 45 minutes and another pipe can fill it in 30 minutes. if these two pipes are open and a third pipe is draining water from the tank, it takes 27 minutes to fill the tank. How long will it take the third pipe alone to empty a full tank
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tank's capacity be C.
P1 takes 45 min to fill the tank. So in 1 minute, P1 will fill 1/45 of the tank.
Similarly, in 1 minute, P2 will fill 1/30 of the tank.
Together, in 1 minute, they will fill out 1%2F45+%2B+1%2F30+=+5%2F90+=+1%2F18 of the tank.
So, together, they will take 18 minutes to fill the tank - if there was no drainage.
But because of the drainage, they take 27 min. So the effective rate of filling is not 1/18 but 1/27 per min.
Effective rate = Rate of P1 + Rate of P2 - Rate of P3 (drainage pipe)
Substituting,
1%2F27+=+1%2F45+%2B+1%2F30+-+P3
P3 = 1%2F18+-+1%2F27+=+1%2F54
i.e. P3 empties 1/54 of the tank every minute.
So it would take P3 54 minutes to empty a full tank.
:)