aj5105 wrote:Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?
A. 8
B. 10
C. 12
D. 15
E. 20
We are given that three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours.
We can let r, s and t be the times, in hours, for printing presses R, S and T to complete the job alone at their respective constant rates. Thus, the rate of printing press R = 1/r, the rate of printing press S = 1/s, and the rate of printing press T = 1/t. Recall that rate = job/time and, since they are completing one printing job, the value for the job is 1. Since they complete the job together in 4 hours, the sum of their rates is 1/4, that is:
1/r + 1/s + 1/t = 1/4
We are also given that printing presses S and T, working together at their respective constant rates, can do the same job in 5 hours. Thus:
1/s + 1/t = 1/5
We can substitute 1/5 for 1/s + 1/t is the equation 1/r + 1/s + 1/t = 1/4 and we have:
1/r + 1/5 = 1/4
1/r = 1/4 - 1/5
1/r = 5/20 - 4/20
1/r = 1/20
r = 20
Thus, it takes printing press R 20 hours to complete the job alone.
Answer:
E
