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Pumps A, B, and C operate at their respective constant [#permalink]
21 May 2008, 05:31

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Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours, pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank?

Ok this one is hard to explan as I use the PR method for work problems (aka Plumber's butt) basically it is a way to show work rate and time in a visual method.

so here we go. I gave the pool a capacity of 10 gallons (you can use any capacity).

First statement tells us 10/(6/5) = rate A+B or A+B = 50/6 Second tells us 10/(3/2) = rate of A+C 0r A+C = 40/6 final statement tells us 10/2 = rate of B+C (to keep numbers easy) 30/6 or B+C = 30/6

Now you have three equations. A+B = 50/6; A+C = 40/6; B+C = 30/6

combine the first two to get B-C= 10/6 then combine with the next one and you get 2B = 40/6 => B= 20/6

now that you have B plug back into your original equations and you get these rates.

A=30/6 B=20/6 C=10/6

A+B+C = 10 gallons per hour or (60/6) because I used 10 as the capacity of the pool it will take them 1 hr together.

****The explanation is far more complicated than it seems, I really like the PR method for solving work problems it is a good way to keep up with your work*****

Great Question I don't think you will see harder work problems on the real thing. +1

Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours, pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank?

1/3 1/2 2/3 5/6 1

I tried solving by subtracting/adding

1/A+1/B=6/5

1/A+1/C=3/2

1/B+1/C=2

We want 1/A+1/B+1/C

I cant seem to get this correct though my numbers keep getting really screwed up.

Well I had to explain it in a detailed way which is a little different than the way I did it -but the PR method works and it's fast. I'd say it only took 1-2 mins.