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Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]
11 Aug 2011, 07:40

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Difficulty:

95% (hard)

Question Stats:

49% (06:32) correct
51% (02:44) wrong based on 108 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?

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]
11 Aug 2011, 08:18

1

This post received KUDOS

KunalPratap wrote:

T can work laone and finishes job in 6 hours, P & J can do the same independently in 3 and 2 hours each. P starts working and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and thet finish the job together. What was freaction of job done by P????

1) 1/9 2) 1/6 3) 1/3 4) 7/18 5) 4/9

Please correct your question. Who starts and who joins? _________________

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]
14 Aug 2011, 00:57

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.

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]
31 Oct 2011, 22:01

1

This post received KUDOS

Expert's post

1

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KunalPratap wrote:

T can work alone and will finish job in 6 hours, P & J can do the same independently in 3 and 2 hours each. T starts working alone and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and they finish the job together. What was fraction of job done by T????

1) 1/9 2) 1/6 3) 1/3 4) 7/18 5) 4/9

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.

Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]
16 Aug 2014, 21:21

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Re: Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]
17 Aug 2014, 02:53

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Expert's post

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fluke wrote:

KunalPratap wrote:

T can work laone and finishes job in 6 hours, P & J can do the same independently in 3 and 2 hours each. P starts working and after 1 hour P joins, both of them work for another 1 hour. After that J joins them and thet finish the job together. What was freaction of job done by P????

1) 1/9 2) 1/6 3) 1/3 4) 7/18 5) 4/9

Please correct your question. Who starts and who joins?

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.

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