Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 05:53

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 17 Jan 2012
Posts: 41
GMAT 1: 610 Q43 V31
Followers: 1

Kudos [?]: 165 [3] , given: 16

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

### Show Tags

27 Jan 2012, 13:19
3
KUDOS
20
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

61% (02:59) correct 39% (01:57) wrong based on 677 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?

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

[Reveal] Spoiler:
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.

Total Job done by Peter = 1/3+1/9 = 4/9

Is there a shorter or quicker way to do it?
[Reveal] Spoiler: OA

Last edited by abhimahna on 28 Oct 2016, 04:17, edited 1 time in total.
Hided the OE
Math Expert
Joined: 02 Sep 2009
Posts: 39049
Followers: 7753

Kudos [?]: 106521 [16] , given: 11627

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

### Show Tags

27 Jan 2012, 13:55
16
KUDOS
Expert's post
13
This post was
BOOKMARKED
docabuzar wrote:
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.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39049
Followers: 7753

Kudos [?]: 106521 [2] , given: 11627

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

### Show Tags

25 Jun 2012, 10:02
2
KUDOS
Expert's post
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

_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23
Followers: 26

Kudos [?]: 468 [8] , given: 11

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

### Show Tags

15 Nov 2012, 01:15
8
KUDOS
2
This post was
BOOKMARKED
First hour with Tom working: $$W=\frac{1}{6}(1)=\frac{1}{6}$$
Second hour with Peter and Tom: $$W=\frac{1}{6}+\frac{1}{3}=1/2$$

Remaining work:$$W=1-\frac{1}{6}-\frac{1}{2}=1/3$$

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 $$1\frac{1}{3}hr==>W=\frac{1}{3}(1\frac{1}{3})=\frac{4}{9}$$

_________________

Impossible is nothing to God.

Intern
Joined: 22 Aug 2013
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 2

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

### Show Tags

24 Aug 2013, 02:38
mbaiseasy wrote:
First hour with Tom working: $$W=\frac{1}{6}(1)=\frac{1}{6}$$
Second hour with Peter and Tom: $$W=\frac{1}{6}+\frac{1}{3}=1/2$$

Remaining work:$$W=1-\frac{1}{6}-\frac{1}{2}=1/3$$

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 $$1\frac{1}{3}hr==>W=\frac{1}{3}(1\frac{1}{3})=\frac{4}{9}$$

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.
MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4333
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Followers: 441

Kudos [?]: 3192 [2] , given: 2306

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

### Show Tags

24 Aug 2013, 03:05
2
KUDOS
Expert's post
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 $$\frac{4}{9}$$
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15509
Followers: 651

Kudos [?]: 210 [0], given: 0

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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15509
Followers: 651

Kudos [?]: 210 [0], given: 0

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.
_________________
Director
Joined: 10 Mar 2013
Posts: 597
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 17

Kudos [?]: 357 [2] , given: 200

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

### Show Tags

29 Nov 2015, 13:14
2
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.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15509
Followers: 651

Kudos [?]: 210 [0], given: 0

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.
_________________
Manager
Joined: 20 Jan 2017
Posts: 65
Location: United States (NY)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
Followers: 2

Kudos [?]: 5 [0], given: 15

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

### Show Tags

03 Feb 2017, 07:26
T-1/6
P-2/6
J-3/6

1*1/6+1*(1/6+2/6)+x(1/6+2/6+3/6)=1
4/6+x*1=1
x=2/6=1/3

P=2/6+2/6*1/3=2/6+2/18=8/18=4/9

Posted from my mobile device
Intern
Joined: 09 Oct 2016
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 2

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.
Joined: 03 Aug 2016
Posts: 113
GPA: 3.9
WE: Information Technology (Consumer Products)
Followers: 3

Kudos [?]: 25 [0], given: 28

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.
_________________

My MBA Journey - https://smalldoubledouble.com

Intern
Joined: 13 Aug 2015
Posts: 25
GPA: 3.82
Followers: 0

Kudos [?]: 16 [0], given: 45

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

### Show Tags

27 May 2017, 18:50
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.

_________________

If you like my posts, Please give kudos. Help me unlock gmat club tests.

Re: Tom, working alone, can paint a room in 6 hours. Peter and   [#permalink] 27 May 2017, 18:50
Similar topics Replies Last post
Similar
Topics:
2 Working alone, Bud can complete a particular task in 6 hours. Lou, wor 3 03 May 2017, 22:05
Kathleen can paint a room in 3 hours, and Anthony can paint an identic 6 13 Apr 2016, 22:54
6 Cameron can paint a room in c hours. Cameron and Mackenzie, working to 13 08 Feb 2017, 13:54
11 Working alone at a constant rate, Alan can paint a house in a hours. 11 30 Jan 2017, 04:35
10 Tom, working alone, can paint a room in 6 hours. Peter and 17 20 Dec 2016, 19:49
Display posts from previous: Sort by