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
Let the job = 8 pages.
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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