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Posts: 4
Updated on: 24 Sep 2014, 04:47
Originally posted by KunalPratap on 11 Aug 2011, 07:40.
Last edited by Bunuel on 24 Sep 2014, 04:47, edited 3 times in total.
Last edited by Bunuel on 24 Sep 2014, 04:47, edited 3 times in total.
Renamed the topic, edited the question and added the OA.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
57% (02:43) correct
43%
(02:56)
wrong
based on 331
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
fluke
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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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.
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.
General Discussion
KunalPratap
Please correct your question. Who starts and who joins?
eragotte
Joined: 02 Feb 2011
Last visit: 12 Dec 2017
Posts: 78
Status:Quant 50+?
Concentration: Strategy, Finance
Schools: Darden '16 Tuck '16
Schools: Darden '16 Tuck '16
Posts: 78
amit2k9
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?
eragotte
Same here. got D. Would be happy for an explanation if OA is E.
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:
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:
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.
1/6+1/6+1/18=7/18.
I got 7/18 toooo
could anyone plz explain why the answer is 4/9??
could anyone plz explain why the answer is 4/9??
KunalPratap
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.
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kostyan5
Joined: 29 Oct 2011
Last visit: 27 Apr 2021
Posts: 114
Concentration: General Management, Technology
Schools: Sloan '16 (D)
GMAT 1: 760 Q49 V44
GPA: 3.76
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.
(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.
I too also got D 7/18
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?
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.
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.
Posts: 107
Yea even I used a logic similar to the one you used Baten80. Got 4/9. Is that the OA though
Posts: 107
D should be the answer. E is wrong.
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