Carcass wrote:
Two machines working on a task can complete a job in 2 hours and 5 hours, respectively. How many hours does it take the two machines, working together but independently, to complete the same task?
(A) 2/5
(B) 7/10
(C) 10/7
(D) 3/2
(E) 5/2
Let's assign a "nice value" to the job.
We want a value that works well with 2 hours and 5 hours.
So let's say the job = making 10 widgets.
rate = output/time One machine can complete the job in 2 hours.
10/2 = 5, so that machine makes widgets at a rate of 5 widgets per hour.
The other machine can complete the job in 5 hours.
10/5 = 2, so that machine makes widgets at a rate of 2 widgets per hour.
They're COMBINED rate = 5 widgets per hour + 2 widgets per hour =
7 widgets per hour.
Time = output/rateTime for the COMBINED machines to make 10 widgets = 10/
7 hours
Answer: C