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## rate problem

This topic has 2 expert replies and 2 member replies
aj5105 Legendary Member
Joined
06 Jul 2008
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#### rate problem

Sat Jan 03, 2009 11:56 am
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

any quick method?

Last edited by aj5105 on Sun Jan 04, 2009 6:59 am; edited 1 time in total

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### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
548 messages
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Fri Dec 08, 2017 7:08 am
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.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
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vivek.kapoor83 Legendary Member
Joined
04 Aug 2008
Posted:
833 messages
13
Sun Jan 04, 2009 11:16 pm
another method,picking no,
let total work - 60unit
total work done in 4hrs , so 1 hr output by all three - 15 unit.
S+T = 60/5 = 12unit work in 1 hr
So, in 1 hr all 3 do - 15 unit
S+t = 12 unit , that means r = 3 unit /hr

So, total work -60 unit
3unit /hr
then 20 hr wil take R to complete the work alone

It is the fastest i think it can be done in 30 sec .....i feel

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
548 messages
Followed by:
3 members
43
Fri Dec 08, 2017 7:08 am
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.

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

vivek.kapoor83 Legendary Member
Joined
04 Aug 2008
Posted:
833 messages
13
Sun Jan 04, 2009 11:16 pm
another method,picking no,
let total work - 60unit
total work done in 4hrs , so 1 hr output by all three - 15 unit.
S+T = 60/5 = 12unit work in 1 hr
So, in 1 hr all 3 do - 15 unit
S+t = 12 unit , that means r = 3 unit /hr

So, total work -60 unit
3unit /hr
then 20 hr wil take R to complete the work alone

It is the fastest i think it can be done in 30 sec .....i feel

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