# A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

(A) 3
(B) 4
(C) 6
(D) 9
(E) 12

This is from the free Official GMAT prep tests 1 and 2 so if you haven’t done those yet: avoid this explanation. This is a work and rate question (cooperative rate). This specific type, adding a certain number of machines to get a job done faster, is not uncommon. I find the easiest way to approach is to get the cooperative rate of the machines by adding the rate of type R and type S. Why do we add? Well, they’re working together on the same project. You subtract if they work against each other (you clean the apartment, your roommate messes it up). In this case the cooperative rate is 1/12. Put that in the T with a variable to count how many 1/12ths you need to get 1 job done in 2 hours. Here’s a tougher version of this type of cooperative work and rate question. And here are a couple more similar questions from the GMAT prep software:

Official GMAT Work and Rate – Cooperative Rate 1

Official GMAT Work and Rate – Cooperative Rate 2

Here’s another set of cooperative work and rate questions to practice on:

Work and Rate 1

Work and Rate 2

Work and Rate 3

Work and Rate 4

Work and Rate 5

For more distance, work, and rate examples you can also check out our GMAT Question of the Day page