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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

by swerve » Mon Aug 13, 2018 10:28 am

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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.

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Source: Beat The GMAT — Problem Solving | Mon Aug 13, 2018 10:28 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue Aug 14, 2018 5:15 am

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.

We're told that S and T can do the full job in 5 hours. So, in working together with R for 4 hours, they must complete 4/5 of the total job themselves.

That leaves 1/5 of the job for R to do in the 4 hours, implying that R could do the whole job in [spoiler] 5 x 4 = 20, E[/spoiler]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Aug 14, 2018 6:06 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Aug 14, 2018 6:30 am

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

Let the job = 20 pages.
Since R+S+T take 4 hours to print the 20-page job, the combined rate for R+S+T = 20/4 = 5 pages per hour.
Since S+T take 5 hours to print the 20-page job, the combined rate for S+T = 20/5 = 4 pages per hour.
R's rate = (rate for R+S+T) - (rate for S+T) = 5-4 = 1 page per hour.
Since R's rate = 1 page per hour, R's time to print the 20-page job = 20/1 = 20 hours.

The correct answer is E.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Sat Aug 18, 2018 6:40 pm

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

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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brushmyquant: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Fri May 27, 2016 8:33 am; Location: Bangalore; GMAT Score:700

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

by brushmyquant » Wed Nov 16, 2022 10:04 am

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 = 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 = 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) = 1/4 - 1/5 = 1/20
=> R = 1/20

R * Time = 1
=> (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

https://www.youtube.com/watch?v=dRxzi_x3ZwY