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?
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Work Rate
Source: Beat The GMAT — Problem Solving |
since A does it in 6 hrs, B in 3 and C in 2... i fixed an amount as the 'work rate'.... 18.
so pr hour a does 1/6 of the job, b 1/3 and c 1/2.
after a working alone, we still have 15 to be done
b+a= 9, so we have 6 left
a+b+c=18
if they do 18 in an hour, they will do 6 in 20min.
so b has workd 6hrs with a and with the others 2
6+2/18= 4/9
not 7/18 as i had said before....
so pr hour a does 1/6 of the job, b 1/3 and c 1/2.
after a working alone, we still have 15 to be done
b+a= 9, so we have 6 left
a+b+c=18
if they do 18 in an hour, they will do 6 in 20min.
so b has workd 6hrs with a and with the others 2
6+2/18= 4/9
not 7/18 as i had said before....
We know the respective rates for Tom, Peter, and John.
Tom: 1/6 Job/Hr
Peter: 1/3 Job/Hr
John: 1/2 Job/Hr
First Hour:
Tom Completes 1/6 of the Job
Second Hour:
Tom Completes 1/6 of the Job
Peter Completes 1/3 of the Job
What fraction of the job must still be completed?
1 - (1/6 - 1/6 - 2/6) = 1/3
Peter's share of this fraction (all three are working together):
(1/3) / (1/3 + 1/6 + 1/2) = 1/3
Peter's fraction of the whole job:
1/3 + (1/3)(1/3)
= 4/9
Tom: 1/6 Job/Hr
Peter: 1/3 Job/Hr
John: 1/2 Job/Hr
First Hour:
Tom Completes 1/6 of the Job
Second Hour:
Tom Completes 1/6 of the Job
Peter Completes 1/3 of the Job
What fraction of the job must still be completed?
1 - (1/6 - 1/6 - 2/6) = 1/3
Peter's share of this fraction (all three are working together):
(1/3) / (1/3 + 1/6 + 1/2) = 1/3
Peter's fraction of the whole job:
1/3 + (1/3)(1/3)
= 4/9
-
PussInBoots
- Master | Next Rank: 500 Posts
- Posts: 157
- Thanked: 3 times
We know the respective rates for Tom, Peter, and John.
Tom: 1/6 Job/Hr
Peter: 1/3 Job/Hr
John: 1/2 Job/Hr
First Hour:
Tom Completes 1/6 of the Job.
Second Hour:
Tom Completes 1/6 of the Job
Peter Completes 1/3 of the Job
What fraction of the job must still be completed?
1 - (1/6 - 1/6 - 2/6) = 1/3
How long does it take for three of them to finish the job?
1/6 + 1/3 + 1/2 = (1/3) / x
1 = 1/3 / x => x= 1/3
Peter's share = 1/3 + 1/3 * 1/3 = 4/9
Tom: 1/6 Job/Hr
Peter: 1/3 Job/Hr
John: 1/2 Job/Hr
First Hour:
Tom Completes 1/6 of the Job.
Second Hour:
Tom Completes 1/6 of the Job
Peter Completes 1/3 of the Job
What fraction of the job must still be completed?
1 - (1/6 - 1/6 - 2/6) = 1/3
How long does it take for three of them to finish the job?
1/6 + 1/3 + 1/2 = (1/3) / x
1 = 1/3 / x => x= 1/3
Peter's share = 1/3 + 1/3 * 1/3 = 4/9
I didnt understand how the below was arrived at:
what is x referring to?
what is x referring to?
PussInBoots wrote:
How long does it take for three of them to finish the job?
1/6 + 1/3 + 1/2 = (1/3) / x
1 = 1/3 / x => x= 1/3
Peter's share = 1/3 + 1/3 * 1/3 = 4/9
-
harshavardhanc
- Legendary Member
- Posts: 526
- Location: India
- Thanked: 68 times
- GMAT Score:680
%ages and fractions.jainrahul1985 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?
T completes 16.66% in one hour, P completes 33.33% in one hour, and J completes 50% in one hour.
one hour after T starts, work done = 16.66%
T and P can complete (16.66 + 33.33) = 50% in one hour, so after two hours total work done = 50 + 16.66 = 66.66%
work remaining = 33.33% or 1/3rd.
together T,P, and J can complete 100% in one hour.
So, time required to complete 1/3 of the work = 1/3 hours. In these 1/3 hours, P will complete 1/3 *1/3 = 1/9th of the work.
therefore, total work done by P = 1/3 (in the second hour) + 1/9 (in the third hour)= 4/9.
Regards,
Harsha
Harsha
T can finish in 1/6 of the room in 1 hr
P can finish in 1/3 of the room in 1 hr
J can finish in 1/2 of the room in 1 hr
After tom works for 1 hour, 1/6th of the painting is completed and remainder is 5/6th
Tom and P working together can finish (1/6 + 1/3) or 3/6th of the room in 1 hour and hence 2/6th of the painting remains
Tom, Pete & John working together can finish the complete room in (1/6+1/3+1/2) in an hour. So 2/6th or 1/3rd of the room can be completed in 1/3 hours.
Pete hence does 1/3 * 1/3 part working with the other 2
Total work that peter does = 1/3*1/3 + 1/3 = 1/9+1/3 = 4/9
P can finish in 1/3 of the room in 1 hr
J can finish in 1/2 of the room in 1 hr
After tom works for 1 hour, 1/6th of the painting is completed and remainder is 5/6th
Tom and P working together can finish (1/6 + 1/3) or 3/6th of the room in 1 hour and hence 2/6th of the painting remains
Tom, Pete & John working together can finish the complete room in (1/6+1/3+1/2) in an hour. So 2/6th or 1/3rd of the room can be completed in 1/3 hours.
Pete hence does 1/3 * 1/3 part working with the other 2
Total work that peter does = 1/3*1/3 + 1/3 = 1/9+1/3 = 4/9
