Carcass wrote:
Machine X if operating alone takes 10 hours to complete a job. Machine Y starts the job one hour after Machine X started the job and X and Y together complete the job in 7 hours. How long does it take for Machine Y to complete the job if it had operated alone?
A. 20 hours
B. 25 hours
C. 31.5 hours
D. 32 hours
E. 35 hours
For work questions when the "job" is not defined, I find it easiest to
assign a nice value to the job.
In this case, I want to find a nice value that works well with the given information (10 hours and 7 hours)
So, let's say the job consists of making a total of
70 widgets (notice that
70 is the least common multiple of 10 and 7)
Given: Machine X if operating alone takes 10 hours to complete a job.In other words, working alone, Machine X can make
70 widgets in 10 hours.
Rate = output/time
So, Machine X's rate =
70/10 =
7 widgets per hour
Given: Machine Y starts the job one hour after Machine X started the job and X and Y together complete the job in 7 hours. In the first hour (while working alone), machine X produces
7 widgets.
70 -
7 =
63So, when Machine Y starts helping, the two machines must make
63 widgets in order to complete the job.
We're told the two machines (working together) complete the job in 7 hours.
Rate = output/time
So the COMBINED rate of the two machines =
63/7 = 9 widgets per hour.
Machine X's rate =
7 widgets per hour
So, we can conclude that Machine Y's rate =
2 widgets per hour
Question: How long does it take for Machine Y to complete the job if it had operated alone?Time = output/rate
So, the time =
70/
2 = 35 hours
Answer: E