Three printing presses, R, S, and T, working together at the

=1/4-1/5=1/20

r can do 1/20 job in 1 hour
r can do the whole job in 20 hours.

1/R+1/S+ 1/T = 1/4
1/S+ 1/T = 1/5
1/R=1/4-1/5
R=20

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



This is my nightmare . I remember studying some formula for combined work in my school days, but forgot. And so everytime , I come across such sums, my brain looks for the formula and fails . Even after trying to work it in RTD method , I am not able to solve. Somebody please help.

This is how I solved the problem:
4 hours * (rate of R + rate of S + rate of T) = total job
5 hours * (rate of S + rate of T) = total job

equate the two, reduce them.

4*rate of R = rate of S + rate of T

Plug back into equation 2: 5*(4*rate of R) = total

20* rate of R = total

\(\frac{1}{r} + \frac{1}{s} + \frac{1}{t} = \frac{1}{4}\)

\(\frac{1}{r} + \frac{1}{s} = \frac{1}{5}\) \(thus ->\) \(\frac{1}{5} + \frac{1}{t} = \frac{1}{4}\)

\(\frac{1}{t} = \frac{1}{4} - \frac{1}{5}\)

\(\frac{1}{t} = \frac{5}{20} - \frac{4}{20}\)


\(t = 20\)

Even though this is a relatively easy question, it gives us the opportunity to practice a number of my GMAT timing tips (the links below include growing lists of questions that you can use to practice each tip):

Rate problems: Use D = R x T and W = R x T
Like most work rate problems, we can start with the equation W = R x T and then plug in the work, rate, and time for each scenario that we are considering.

Set the amount of work equal to 1 for a single job
Because we’re talking about a single printing job, we just set W = 1 for each scenario.

Add rates when they are simultaneous
Let’s define variables for the rates for printing presses R, S, and T as Rr, Rs, and Rt. Remember that we can add rates when they are simultaneous, so, when all 3 presses are working together, the rate is Rr + Rs + Rt. When just S and R are working together, the rate is Rs + Rt.

Rate and time are reciprocals of each other for a single job
Since we are given the amounts of time for each scenario, we can set the rate equal to the reciprocal of the time for each scenario. This means that Rr + Rs + Rt = 1/4 and Rs + Rt = 1/5. In addition, we are solving for the time it takes printing press R to do the job working alone; if we call this time Tr, then Tr = 1/Rr, and we can solve for Tr if we know Rr.

Eliminate combinations of variables using substitution
While we can’t solve for Rs and Rt separately, we don’t have to. Since we know their sum Rs + Rt = 1/5, we can just plug this value in for (Rs + Rt) in the equation Rr + Rs + Rt = 1/4. This is enough to allow us to solve for Rr, which then allows us to solve for Tr, which is the final answer to this question.

Please let me know if you have any questions, or if you want me to post a video solution!

Video solution from Quant Reasoning:
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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:

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

Answer: Option E

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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?

We can use LCM method to solve this time & work related question.

Total work = LCM( 4,5) = 20 units.

Per hour work of R,S, and T = 20/4 = 5 units

Per hour work of S, and T = 20/5 =4 units

So, we can conclude that Per hour work of R = 5 -4 = 1 unit.

The time taken by R, working alone to do the same job = 20/1 = 20 hrs

Option E is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME

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

Using, Rate * Time = Work Done

Let Rate of R be R, S be S and T be T and Let the work done = 1

If they work together then their combined rate = R + S + T

=> (R + S + T) * 4 = 1
=> R + S + T = \(\frac{1}{4}\) ...(1)

S and T, working together at their respective constant rates, can do the same job in 5 hours.

=> (S + T) * 5 = 1
=> S + T = \(\frac{1}{5}\) ...(2)

How many hours would it take R, working alone at its constant rate, to do the same job?

(1) - (2) we get

R + S + T - (S + T) = \(\frac{1}{4}\) - \(\frac{1}{5}\) = \(\frac{5}{20}\) - \(\frac{4}{20}\) = \(\frac{1}{20}\)
=> R = \(\frac{1}{20}\)

R * Time = 1
=> \(\frac{1}{20}\) * Time = 1
=> Time = 20 hours

So, Answer will be E
Hope it helps!

Watch the following video to learn How to Solve Work Rate Problems

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