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, 12:19

3

This post received KUDOS

16

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

62% (02:56) correct
38% (01:39) wrong based on 514 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.

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

Show Tags

29 Nov 2015, 12:14

2

This post received KUDOS

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 !

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 \(\frac{4}{9}\)
_________________

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.

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

Show Tags

07 Sep 2014, 21:20

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, 06:15

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.
_________________

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...