Three copying machines A, B, and C, working together at their respective constant rates, can do a copying work in 2 hours. B and C, working together at their respective constant rates, can do the same copying job in 4 hours. How many hours would it take A, working alone at its constant rate, to do the same job?
A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
The OA is C.
Source: e-GMAT
Three copying machines A, B, and C, working together at
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Let the job = 8 pages.swerve wrote:Three copying machines A, B, and C, working together at their respective constant rates, can do a copying work in 2 hours. B and C, working together at their respective constant rates, can do the same copying job in 4 hours. How many hours would it take A, working alone at its constant rate, to do the same job?
A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
Since A+B+C take 2 hours to copy the 8-page job, the combined rate for A+B+C = 8/2 = 4 pages per hour.
Since B+C take 4 hours to copy the 8-page job, the combined rate for B+C = 8/4 = 2 pages per hour.
A's rate = (rate for A+B+C) - (rate for B+C) = 4-2 = 2 pages per hour.
Since A's rate = 2 pages per hour, A's time to copy the 8-page job = 8/2 = 4 hours.
The correct answer is C.
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Let a, b, and c be the number of hours A, B, and C take to finish the job alone, respectively. Their respective rates are 1/a, 1/b, and 1/c. We have:swerve wrote:Three copying machines A, B, and C, working together at their respective constant rates, can do a copying work in 2 hours. B and C, working together at their respective constant rates, can do the same copying job in 4 hours. How many hours would it take A, working alone at its constant rate, to do the same job?
A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
The OA is C.
Source: e-GMAT
1/a + 1/b + 1/c = 1/2
and
1/b + 1/c = 1/4
Subtracting the second equation from the first, we have:
1/a = 1/4
a = 4
Answer: C
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