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, 13:19

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Question Stats:

59% (03:33) correct

40% (01:45) wrong

based on 55 sessions

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?

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Re: Working Retes [#permalink]

27 Jan 2012, 13:55

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docabuzar wrote:

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.
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tom working alone can paint [#permalink]

25 Jun 2012, 09:58

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 [#permalink]

25 Jun 2012, 10:02

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shradhagrover18 wrote:

Merging similar topics. Please ask if anything remains unclear.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html
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Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]

15 Nov 2012, 01:15

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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}

Answer:E

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink] 15 Nov 2012, 01:15

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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

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