BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:10 am

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

Answer: A
Source: Official guide

Another way to solve this question is to assign a nice value to the job.
So, we want to use a value that works well with the given numbers in the question (9, 3 and 4 hours).
Since 36 is the least common multiple of 9, 3 and 4, let's say the entire job consists of making 36 widgets

Machine X can complete a certain job in 9 hours
So, Machine X's RATE = 36/9 = 4 widgets per hour

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.
At its rate of 4 widgets per hour, Machine X would have produced 12 widgets in 3 hours
36 - 12 = 24
So, after the first 3 hours, the two machines would need to produce the 24 remaining widgets in the job

Since the two machines COMBINED produced the remaining 24 in 4 hours, their COMBINED RATE = 24/4 = 6 widgets per hour

We can write: (Machine X's rate) + (Machine Y's rate) = 6 widgets per hour
Substitute to get: 4 + (Machine Y's rate) = 6 widgets per hour
From this, we can see that Machine Y's rate = 2 widgets per hour

How many hours would it have taken machine Y, working alone, to complete the entire job?
time = output/rate
So, time = 36/2 = 18

Answer: A

Cheers,
Brent