Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

27 Jan 2012, 13:19

3

This post received KUDOS

22

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

63% (01:54) correct
37% (01:54) wrong based on 763 sessions

HideShow timer Statistics

Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?

First Hr : T starts working and in 1 hour can finish 1/6 of the job

Second Hr: T & P starts working and in an hr can finish 1/6+1/3 = 3/6 of the job. So Total 4/6 of the job is finished by now

Third Hr: T,P & J starts working but they have only 2/6 of the job remaining. Working together they need one hr to finish the entire job (work formula 1/6+1/3+1/2 = 1/1 = 1 hr) so they work only for 2/6 of an hour. THerefore peter working at a rate of 1/3 can do only 1/3*2/6 = 1/9 of the job before the job is finished.

Tom, working alone, can paint a room in 6 hours. Peter and John, working independently, can paint the same room in 3 hours and 2 hours, respectively. Tom starts painting the room and works on his own for one hour. He is then joined by Peter and they work together for an hour. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. What fraction of the whole job was done by Peter?

A. 1/9 B. 1/6 C. 1/3 D. 7/18 E. 4/9

Let the time when all three were working together be t hours. Then: Tom worked for t+2 hour and has done 1/6*(t+2) part of the job; Peter worked for t+1 hour and has done 1/3*(t+1) part of the job; John worked for t hours and has done 1/2*t part of the job:

1/6*(t+2)+1/3*(t+1)+1/2*t=1 --> multiply by 6 --> (t+2)+(2t+2)+3t=6 --> t=1/3;

Hence Peter has done 1/3*(1/3+1)=4/9 part of the job.

tom working alone can paint a room in 6 hours. peter and john , working independently, can paint the same room in 3 hours and 2 hours , respectively. tom starts painting the room and works on his own for one hour. he is then joined by peter and they work together for an hour. finally, john joins them and the three of them work together to finish the room, each one working at his respective rate. what fraction of the whole job was done by peter ?

a. 1/9 b. 1/6 c. 1/3 d. 7/18 e. 4/9

Merging similar topics. Please ask if anything remains unclear.

time left with all three: \(\frac{1}{6}+\frac{1}{3}+\frac{1}{2}(t)=1/3==>t=\frac{1}{3}hr\)

Therefore, Peter worked for \(1\frac{1}{3}hr==>W=\frac{1}{3}(1\frac{1}{3})=\frac{4}{9}\)

Answer:E

Could you please explain after the 1/3 remaining. I understood until all 3 complete 1 work together,so from this point on wards what is the work remaining ?

Previous case tom and peter complete (1/6+1/3) in one hour so total work completed is (1/6+1/2) is 2/3 , now when peter,tom and jack together work (1/6+1/2+1/3) is 1.Does that mean work gets completed when peter comes in,should the work be added 2/3+1 .

1/3 work is to be completed so how do you proceed from here. Thanks.

Tom, working alone, can paint a room in 6 hours. :- Tom is finishing 100/6 i.e. 16.66% of the work in 1 hour.

Peter, working independently, can paint the same room in 3 hours. :- Peter is finishing 100/3 i.e. 33.33% of the work in 1 hour.

John, working independently, can paint the same room in 2 hours. :- Tom is finishing 100/2 i.e. 50% of the work in 1 hour.

Tom starts painting the room and works on his own for one hour. :- Tom Completed 16.66 of the work. 83.34% work is balance

He is then joined by Peter and they work together for an hour. :- Tom + Peter Completed (16.66% + 33.33% = 50%) of the work. 33.33% work is balance Finally, John joins them and the three of them work together to finish the room :- Together Tom + Peter + John Complete (16.66% + 33.33% + 50= 100%) work in 1 hour, So to finish balance 33.33% work it would take them \(\frac{33.33}{100} = \frac{1}{3} hour.\)

What fraction of the whole job was done by Peter? :- We know Peter worked for \(1 + \frac{1}{3} hour.\) He must have completed \(33.33 + \frac{1}{3}(33.33)\) work ------> He completed 44.44% work which equals to \(\frac{4}{9}\)
_________________

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

07 Sep 2014, 22:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

09 Sep 2015, 07:15

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

29 Nov 2015, 13:14

2

This post received KUDOS

1

This post was BOOKMARKED

Let's use smart numbers here --> Work=18 Rate * Time = Work Tom: 3 x 6 = 18 Peter: 6 x 3 = 18 John: 9 x 2 = 18

Before John joined Tom and Peter: Tom worked 2 Hours -> 2*3=6 and Peter 1*6=6 gives us 12. So we are left with 18-12=6 for all three of them --> (3+6+9)*t=6, thus t=1/3 this means that Peter worked 2+1/3 Hours = 6+2=8 --> 8/18=4/9 At least this approach helps me... Don't like dealind with fractions when you're tired.
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

12 Jan 2017, 15:01

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

07 Apr 2017, 13:54

Let`s first put some value to the area of the room to make this problem easier to solve. We are looking for a value that is advisable by the working rate of each one, Tom =6, Peter = 3, and John = 2. So the best value for the room area is 6x3x2 = 36 feet. Tom starts painting the room and works on his own for one hour, so he paint 6 feet of the room, and 30 feet is the remaining. He is then joined by Peter and they work together for an hour, so Tom paint another 6 feet, Peter paint 12 feet, and 30 – 6 -12 = 12 feet is the remaining. Finally, John joins them and the three of them work together to finish the room, each one working at his respective rate. Here we need to divide the remaining 6 feet among Tom, Peter and John based on their working rate. Tom = 12/6 = 2 feet, Peter = 12/3 = 4 feet, and John = 12/2 =6feet. What fraction of the whole job was done by Peter? Peter fraction = (12+4)/36 =4/9 ---D

Last edited by nawaf52 on 08 Apr 2017, 20:20, edited 1 time in total.

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

07 Apr 2017, 14:03

So i used different approach. I wasnt able to solve it, but brought it down to two options. If peter worked for one hour thats 33% of work and he worked with tom n john after that so technically he finished more than 33%. That eliminates A,B and C.

And then i guessed D. I know its a wrong answer but better chance at guessing out of 2 than out of 5.
_________________

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

Show Tags

27 May 2017, 18:50

1

This post was BOOKMARKED

Tom's individual rate is 1 job / 6 hours or 1/6. During the hour that Tom works alone, he completes 1/6 of the job (using rt = w).

Peter's individual rate is 1 job / 3 hours. Peter joins Tom and they work together for another hour; Peter and Tom's respective individual rates can be added together to calculate their combined rate: 1/6 + 1/3 = 1/2. Working together then they will complete 1/2 of the job in the 1 hour they work together.

At this point, 2/3 of the job has been completed (1/6 by Peter alone + 1/2 by Peter and Tom), and 1/3 remains.

When John joins Tom and Peter, the new combined rate for all three is: 1/6 + 1/3 + 1/2 = 1. The time that it will take them to finish the remaining 1/3 of the job can be solved: rt = w (1)(t) = 1/3 t = 1/3.

The question asks us for the fraction of the job that Peter completed. In the hour that Peter worked with Tom he alone completed: rt = w w = (1/3)(1) = 1/3 of the job. In the last 1/3 of an hour that all three worked together, Peter alone completed: (1/3)(1/3) = 1/9 of the job. Adding these two values together, we get 1/3 + 1/9 of the job = 4/9 of the job.

The correct answer is E.
_________________

If you like my posts, please give kudos. Help me unlock gmatclub tests.

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...