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

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Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]  27 Jan 2012, 12:19
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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

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
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Re: Working Retes [#permalink]  27 Jan 2012, 12:55
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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.

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Re: tom working alone can paint [#permalink]  25 Jun 2012, 09:02
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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

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Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]  15 Nov 2012, 00:15
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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 $$1\frac{1}{3}hr==>W=\frac{1}{3}(1\frac{1}{3})=\frac{4}{9}$$

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Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]  24 Aug 2013, 01:38
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.
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Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]  24 Aug 2013, 02:05
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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 $$\frac{4}{9}$$
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Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]  07 Sep 2014, 21:20
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Re: Tom, working alone, can paint a room in 6 hours. Peter and   [#permalink] 07 Sep 2014, 21:20
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