Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE PS
Solution:
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
