A company has two types of machines, type R and type S

[alexei600]

I am sorry.
I have set up rtd chart. The rate of machine"R" 1/36 and the rate of "S" is 1/18. I summed the rates up to get 1/12. then multiplied by 2 ( hours), and got 1/6. The question is how I get 6 machines form from 1/6 ( 1 job 6 hours)
Thanks.

[RonPurewal]

this is the problem:

then multiplied by 2 ( hours), and got 1/6.

that's a misinterpretation of what you should do with the "2 hours" part.
the post says that the machines together can "do the job in 2 hours"; this means that the overall rate is 1/2. (this is what you do whenever you are given that someone/something can "do 1 job in x hours"; you write "rate = 1/x".)

so, the deal is (1/12) * N = 1/2
N = 6
so, you have 6 of each machine.

[jmiceli0819]

great answers everyone. i just had one question i was hoping someone could answer; i approached the question by taking the combined time ... 12 hours for R & S to complete the task (1 of each) so in essence i thought if we had two it would take 6 hours ... 3 it would take 3 hours ... and so forth ... obviously the answer is wrong but can anyone explain why its wrong? thanks!

[jnelson0612]

great answers everyone. i just had one question i was hoping someone could answer; i approached the question by taking the combined time ... 12 hours for R & S to complete the task (1 of each) so in essence i thought if we had two it would take 6 hours ... 3 it would take 3 hours ... and so forth ... obviously the answer is wrong but can anyone explain why its wrong? thanks!

You're on the right track here.

One R and one S machine can do the job in 12 hours.
Two R and two S machines can do the job in 6 hours.
Four R and four S machines can do the job in 3 hours.
(Notice that by doubling the number of machines I halve the amount of time needed to do the job, as you correctly concluded earlier.)

Okay, so we're close now. Four R machines can do the job in 3 hours (assuming equal number of S machines also working as stated in the problem). However, we want the work done in 2 hours, not 3.

Let's set up an equation: 4 (R machines) * 3 hours = x (R machines) * 2 hours.

We solve for x and it is 6. Thus, 6 R machines are needed to get the job done in 2 hours (obviously along with 6 S machines).