swerve wrote:**Source: Official Guide**

Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8

B. 10

C. 12

D. 15

E. 20

The OA is E.

----------ASIDE--------------------

For work questions, there are two useful rules:

**Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job**
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

**Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job**
Example: If Sam can complete 1/8 of the job

in one hour, then it will take him 8/1 hours to complete the job.

Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

----ONTO THE QUESTION-----------------------

Let R = the numbers of hours for printing press R to complete the ENTIRE task on its own.

Let S = the numbers of hours for printing press S to complete the ENTIRE task on its own.

Let T = the numbers of hours for printing press T to complete the ENTIRE task on its own.

So, from

**rule #1**, 1/R = fraction of the job that R can complete in ONE HOUR

1/S = fraction of the job that S can complete in ONE HOUR

1/T = fraction of the job that T can complete in ONE HOUR

**Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours**
So, from

**rule #1**, the presses (working together) can complete 1/4 of the job in ONE HOUR

In other words:

1/R + 1/S + 1/T = 1/4
**S and T, working together at their respective constant rates, can do the same job in 5 hours.**
So, from

**rule #1**, presses S and T (working together) can complete 1/5 of the job in ONE HOUR

In other words:

1/S + 1/T = 1/5
We now have:

1/R + 1/S + 1/T = 1/4
1/S + 1/T = 1/5
Subtract the bottom equation from the top equation to get: 1/R = 1/4 - 1/5

Simplify: 1/R = 1/20

So, R = 20

** How many hours would it take R, working alone at its constant rate, to do the same job?**
In other words, what is the value of R?

Answer: E

Cheers,

Brent