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Question from Gmat Prep- Help please! 11

by bobdylan » Fri May 04, 2012 9:08 am
Pumps A,B and C operate at their respective constant rates. Pump A and B, operating together, can fill a certain tank in 6/5 hours, pump A and C, operating together, can fill the tank in 3/2 hours, and pump B and C fill the tank in 2 hours. How many hours does it take pumps A,B and C, working together, to fill the tank.
a) 1/3
b)1/2
c)2/3
d)5/6
e) 1
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by Bill@VeritasPrep » Fri May 04, 2012 9:22 am
The first step is to convert times to rates:

T(A+B)=6/5, so R(A+B)=5/6

T(A+C)=3/2, so R(A+C)=2/3 (or 4/6)

T(B+C)=2, so R(B+C)=1/2 (or 3/6)

We can now set up a system of two equations using the rates and subtract the second from the first:

A+B=5/6
A+C=4/6

B-C=1/6

Since we know that B+C=3/6, we can figure out that R(B)=2/6 and R(C)=1/6. From there, we can derive R(A)=3/6

The combined rate of the three machines is 3/6 + 2/6 + 1/6 = 6/6 = 1, which means that A, B, and C can fill the tank in 1 hour.
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by LalaB » Fri May 04, 2012 9:40 am
1/A+1/B=5/6
1/A+1/C=2/3
1/B+1/C=1/2

2(1/A+1/B+1/C)=5/6+2/3+1/2
1/A+1/B+1/C=1

ANS IS E
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by Bill@VeritasPrep » Fri May 04, 2012 9:43 am
LalaB wrote:1/A+1/B=5/6
1/A+1/C=2/3
1/B+1/C=1/2

2(1/A+1/B+1/C)=5/6+2/3+1/2
1/A+1/B+1/C=1

ANS IS E
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by GMATGuruNY » Sat May 05, 2012 3:21 am
bobdylan wrote:Pumps A,B and C operate at their respective constant rates. Pump A and B, operating together, can fill a certain tank in 6/5 hours, pump A and C, operating together, can fill the tank in 3/2 hours, and pump B and C fill the tank in 2 hours. How many hours does it take pumps A,B and C, working together, to fill the tank.
a) 1/3
b)1/2
c)2/3
d)5/6
e) 1
An alternate approach is to plug in a value for the tank.
The advantage is that all of rates and times become integer values.

Let the tank = 6 liters.

Rate for A and B = w/t = 6/(6/5) = 5 liters per hour.
Rate for A and C = w/t = 6/(3/2) = 4 liters per hour.
Rate for B and C = w/t = 6/2 = 3 liters per hour.

Combining the rates above:
(A+B) + (A+C) + (B+C) = 5+4+3 = 12.
2A + 2B + 2C = 12.
A+B+C = 6 liters per hour.

Time for A+B+C = w/r = 6/6 = 1 hour.

The correct answer is E.
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