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Director
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Pumps A, B, and C operate at their respective constant [#permalink]
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21 May 2008, 06:31
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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?
1/3 1/2 2/3 5/6 1



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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 06:56
E.
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 BC= 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



Director
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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:00
I think there is a easier way to solve...I was able to get in quicker, but I can't really explain it...Can a expert tackle this one?



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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:01
jimmyjamesdonkey wrote: 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.



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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:07
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 12 mins.
is the OA =1



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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:09
Also if you don't like the plug in method I used you could use x if it makes more sense to you.
A+B=5x/6 A+C=2x/3 B+C=x/2



Director
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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:17
I solved like this>
A+B = 1/(6/5) A+C = 1/(3/2) B+C = 1/2
Combine:
2a + 2b + 2c = 2
a + b + c = 1
This seems to work, but is it mathematically correct?



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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:22
lsuguy7 wrote: Also if you don't like the plug in method I used you could use x if it makes more sense to you.
A+B=5x/6 A+C=2x/3 B+C=x/2 Make x=1 and it is exactly the same! I just added an X to show how the PR Method works but you don't need it, you basically made the container x=1 the A+B = 5/6 is the rate and so on. So yes it is mathematically correct.



Director
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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:27
lsuguy7, do you have this PR method documented someplace?



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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:30
I don't currently have anything I'll see if I can do a write up on it soon.



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Re: GMATPrep: RTD [#permalink]
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21 May 2008, 07:37
jimmyjamesdonkey wrote: I solved like this>
A+B = 1/(6/5) A+C = 1/(3/2) B+C = 1/2
Combine:
2a + 2b + 2c = 2
a + b + c = 1
This seems to work, but is it mathematically correct? There we go. jeez. i was mking it so hard on myself. That is probably the quickest way to solve this problem. Nice job.










