Tom, working alone, can paint a room in 6 hours. Peter and : Problem Solving (PS)

KunalPratap

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

Updated on: 24 Sep 2014, 05:47

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: tom-working-alone-can-paint-a-room-in-6-hours-peter-and-126629.html

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Originally posted by KunalPratap on 11 Aug 2011, 08:40.
Last edited by Bunuel on 24 Sep 2014, 05:47, edited 3 times in total.

Renamed the topic, edited the question and added the OA.

L

Bunuel

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

17 Aug 2014, 03:53

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Expert Reply

fluke wrote:

KunalPratap wrote:

T can work laone and finishes job in 6 hours, P & J can do the same independently in 3 and 2 hours each. P starts working and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and thet finish the job together. What was freaction of job done by P????

1) 1/9
2) 1/6
3) 1/3
4) 7/18
5) 4/9

Please correct your question. Who starts and who joins?

The proper version of this question is below:
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.

Answer: E.

[color=#ff0000]OPEN DISCUSSION OF THIS QUESTION IS HERE: tom-working-alone-can-paint-a-room-in-6-hours-peter-and-126629.html
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fluke

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Joined: 20 Dec 2010

Posts: 1114

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

11 Aug 2011, 09:18

2

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KunalPratap wrote:

T can work laone and finishes job in 6 hours, P & J can do the same independently in 3 and 2 hours each. P starts working and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and thet finish the job together. What was freaction of job done by P????

1) 1/9
2) 1/6
3) 1/3
4) 7/18
5) 4/9

Please correct your question. Who starts and who joins?

amit2k9

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

12 Aug 2011, 00:15

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1st hour T works = 1/6 work completed = 1/6 remaining work = 5/6

2nd hour T works = 1/6 work completed = 1/6 + 1/3 = 1/2 remaining work = 5/6-1/2 = 1/3

when (1/6+1/3+1/2) all 3 work, it is completed in 1 hr

hence remaining work is completed in 1/3 hr

now in 60 min T completes 1/6 work
in 1/3 = 20 min T completes 1/9 work

thus, 1/6 + 1/6 + 1/9 = 4/9.

hence E.

eragotte

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

12 Aug 2011, 12:15

amit2k9 wrote:

1st hour T works = 1/6 work completed = 1/6 remaining work = 5/6

2nd hour T works = 1/6 work completed = 1/6 + 1/3 = 1/2 remaining work = 5/6-1/2 = 1/3

when (1/6+1/3+1/2) all 3 work, it is completed in 1 hr

hence remaining work is completed in 1/3 hr

now in 60 min T completes 1/6 work
in 1/3 = 20 min T completes 1/9 work

thus, 1/6 + 1/6 + 1/9 = 4/9.

hence E.

I did the same for the first two periods, but then in the third, 1/3 hr is left * T's 1/6th = 1/18, thus 7/18 total.

What am I misunderstanding?

144144

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

12 Aug 2011, 12:45

eragotte wrote:

amit2k9 wrote:

1st hour T works = 1/6 work completed = 1/6 remaining work = 5/6

2nd hour T works = 1/6 work completed = 1/6 + 1/3 = 1/2 remaining work = 5/6-1/2 = 1/3

when (1/6+1/3+1/2) all 3 work, it is completed in 1 hr

hence remaining work is completed in 1/3 hr

now in 60 min T completes 1/6 work
in 1/3 = 20 min T completes 1/9 work

thus, 1/6 + 1/6 + 1/9 = 4/9.

hence E.

I did the same for the first two periods, but then in the third, 1/3 hr is left * T's 1/6th = 1/18, thus 7/18 total.

What am I misunderstanding?

Same here. got D. Would be happy for an explanation if OA is E.

bodleyev

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Schools: CBS '15 (M) Duke '15 (A) HBS '15 (D) Sloan '15 (II) Wharton '15 (D)

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WE:Corporate Finance (Manufacturing)

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

13 Aug 2011, 17:02

1

Kudos

First hour:

T: 1/6 job/hour * 1 hour = 1/6 job

Remaining work: 1 - 1/6 = 5/6 job

Second hour:

T: 1/6 job/hour * 1 hour = 1/6 job
P: 2/6 job/hour * 1 hour = 2/6 job

Remaining work: 5/6 - 3/6 = 2/6 job
T, P, J combined rate: 1 job/hour.
Remaining time to complete 2/6 job: 2/6 job / 1 job/hour = 2/6 hours

T: 1/6 job/hour * 2/6 hours = 2/36 = 1/18 jobs
P: 2/6 job/hour * 2/6 hours = 4/36 = 1/9 jobs
J: 3/6 job/hour * 2/6 hours = 6/36 = 1/6 jobs

Thus T completes 1/6 + 1/6 + 1/18 = (3 + 3 + 1)/18 = 7/18 of the job
P completes 2/6 + 1/9 = (6 + 2)/18 = 8/18 of the job
J completes 1/6 = 3/18 of the job

IMO:

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D

arunrajak

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Location: NYC

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

14 Aug 2011, 01:57

I too got 7/18. If T works for 1 hr and complete 1/6 work then in 20 minutes (1/3 of an hour) T can finish 1/3 of job that T does in 1 hr. So it should be 1/6*1/3=1/18. So total work done by T is:
1/6+1/6+1/18=7/18.

shahideh

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Joined: 25 May 2011

Posts: 60

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

30 Oct 2011, 11:49

I got 7/18 toooo
could anyone plz explain why the answer is 4/9??

L

KarishmaB

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Joined: 16 Oct 2010

Posts: 14815

Location: Pune, India

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

31 Oct 2011, 23:01

1

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Expert Reply

KunalPratap wrote:

T can work alone and will finish job in 6 hours, P & J can do the same independently in 3 and 2 hours each. T starts working alone and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and they finish the job together. What was fraction of job done by T????

1) 1/9
2) 1/6
3) 1/3
4) 7/18
5) 4/9

T alone does the work in 6 hrs so rate = 1/6 work/hr
For P, the rate of work = 1/3 = 2/6 work/hr
For J, the rate of work = 1/2 = 3/6 work/hr
In first hour, T works alone so 1/6 of the work is done.
In the second hour, T and P work so 1/6 + 2/6 = 3/6 of the work is done. Now only 2/6 of the work is left.
In the third hour, they all work together at rate 1 work/hr (1/6+2/6+3/6)
Since only 2/6 of the work is left, time taken = 2/6 hr
Now, we know that T worked for the complete 2(2/6) hrs at the rate (1/6) so work done by T = (1/6)*2(2/6) = 7/18th of the entire work.

Answer is D.

kostyan5

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Schools: Sloan '16 (D)

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

02 Nov 2011, 08:36

Use respective work rates, I got:

(1)*1/6 + (1)*(1/6+2/6) + x*(1/6+2/6+3/6) = 1 (1 whole job)

Solving for x: 4/6 + x = 1 -> x = 2/6 = 1/3

So T worked for a total of 1+1+1/3 = 7/3 hours at the rate of 1/6 jobs per hour.

So T completed 7/3 * 1/6 = 7/18 of one job. Answer is D.

Bowtie

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Concentration: Finance, Strategy

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

13 Nov 2011, 14:01

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I too also got D 7/18

kajolnb

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Joined: 27 May 2011

Posts: 4

Work Rate Problem [#permalink]

01 Dec 2011, 00:09

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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?

P

MHIKER

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Re: Work Rate Problem [#permalink]

01 Dec 2011, 00:23

1

Kudos

Rates:
Tom = 1/6
Peter = 1/3 = 2/6
John = 1/2 = 3/6

1 hours Tom + 1 hour (Tom+Peter) + x hours (Tom+Peter+John) = 1
1/6 + (1/6+1/3) + (1/6+1/3+1/2)*x = 1
1/6 + 1/2 + 6/6*x = 1
x = 1/3 hour
Now, peter work for 1/3*1*3 + 1/3
= 1/9 + 1/3
= 4/9 ans.

siddharthmuzumdar

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Re: Work Rate Problem [#permalink]

22 Dec 2011, 03:09

Yea even I used a logic similar to the one you used Baten80. Got 4/9. Is that the OA though

siddharthmuzumdar

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Joined: 12 Oct 2011

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

05 Jan 2012, 00:55

D should be the answer. E is wrong.

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Re: Work Rate Problem [#permalink]

20 Dec 2016, 19:49

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Re: Work Rate Problem [#permalink]

20 Dec 2016, 19:49

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