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

Question

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

Show Answer

Official Answer

E

Bunuel · Accepted Answer

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

amit2k9 · Answer

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.

fluke · Answer

Please correct your question. Who starts and who joins?

eragotte · Answer

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 · Answer

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

bodleyev · Answer

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:  D

arunrajak · Answer

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 · Answer

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

KarishmaB · Answer

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 · Answer

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 · Answer

I too also got D 7/18

kajolnb · Answer

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

Show Answer

Official Answer

E

MHIKER · Answer

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 · Answer

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

siddharthmuzumdar · Answer

D should be the answer. E is wrong.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards