BTGmoderatorDC wrote:Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours. Machine X worked on the job alone for the first 3 hours and the two machines, working together, then completed the job in 4 more hours. How many hours would it have taken machine Y, working alone, to complete the entire job?
(A) 18
(B) 13 1/2
(C) 7 1/5
(D) 4 1/2
(E) 3 2/3
OA A
Source: Official Guide
Solution:
We see the rate of machine X = 1/9. We can let y = the number of hours it takes for machine Y to complete the entire job by itself. Thus the rate of machine Y = 1/y and we can create the equation:
3(1/9) + 4(1/9 + 1/y) = 1
3/9 + 4/9 + 4/y = 1
7/9 + 4/y = 1
4/y = 2/9
2y = 36
y = 18
Alternate Solution:
When machine Y started working, machine X had been working for 3 hours; therefore, 3/9 = 1/3 of the job was completed. If the two machines completed the remaining 2/3 of the job in 4 hours, they would have completed the whole job in 4/(2/3) = 6 hours. Thus, in one hour, both machines working together complete 1/6 of the job and machine X alone completes 1/9 of the job. Then, machine Y alone completes 1/6 - 1/9 = 1/18 of the job in one hour. It follows that it would take 18 hours for machine Y to complete the job alone.
Answer: A
