rate problem

Let R,S,T be the numbers of hours to complete the whole task individually.
Note: after one hour, R (working alone) will have completed 1/R of the job.

Now determine the amount completed after 1 hour for the two groups.
1/R + 1/S + 1/T = 1/4
1/S + 1/T = 1/5

So, 1/R = 1/4-1/5 = 1/20
So, R = 20

aj5105 wrote: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

We are given that three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours.

We can let r, s and t be the times, in hours, for printing presses R, S and T to complete the job alone at their respective constant rates. Thus, the rate of printing press R = 1/r, the rate of printing press S = 1/s, and the rate of printing press T = 1/t. Recall that rate = job/time and, since they are completing one printing job, the value for the job is 1. Since they complete the job together in 4 hours, the sum of their rates is 1/4, that is:

1/r + 1/s + 1/t = 1/4

We are also given that printing presses S and T, working together at their respective constant rates, can do the same job in 5 hours. Thus:

1/s + 1/t = 1/5

We can substitute 1/5 for 1/s + 1/t is the equation 1/r + 1/s + 1/t = 1/4 and we have:

1/r + 1/5 = 1/4

1/r = 1/4 - 1/5

1/r = 5/20 - 4/20

1/r = 1/20

r = 20

Thus, it takes printing press R 20 hours to complete the job alone.

Answer: E

Hi All,

This prompt starts by telling us that three printing presses (R, S and T) can complete a job TOGETHER in 4 hours. This first sentence implies that we’re dealing with a “Work Formula” question – and there are a couple of different ways to go about solving these types of prompts.

We’re then told that when S and T work together, it takes 5 hours to complete the SAME job. We’re asked how long it would take Press R to complete the job on its own.

Since we’re dealing with more than 2 presses, we should use the “in 1 hour” method to approach this question.

When just press S and T are working, we know that the job is complete in 5 hours; this means that those two presses will complete 1/5 of the job each hour. We can then use that information against what we know about when all 3 machines are working together.

Since that job takes 4 hours to complete – and we know the total amount of work that S and T will do in that 4 hours – we can determine how quickly R works…

In 4 hours, S and T combined will complete (4)(1/5) = 4/5 of the job. Thus, the remaining 1/5 of the job has to be done by Press R. It takes Press R 4 hours to complete that 1/5 of the job, so it would take Press R (4)(5) = 20 hours to complete that entire job on its own.

Final Answer: E

GMAT Assassins aren’t born, they’re made,
Rich