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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]  20 Aug 2007, 18:34
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?

1/9
1/6
1/3
7/18
4/9
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Ok, Tom's rate is 1/6, Peter's rate is 1/3, and John's rate is 1/2
Tom first worked for one hour, therefore 1/6 of the job is done, hence 5/6 left.
Then Peter joins in and they both worked one hour (1/6+1/3)*1=3/6, another 3/6 of the job is done. There are 1-1/6-3/6=2/6 of job left. Then John joins in. (1/6+1/3+1/2)*X=2/6 from this equation you know that it took them 1/3 hour to finish the rest of the job. Therefore, Peter worked a total of 1 and 1/3 hour. It usually took him 3 hours for the whole job, so the fraction he did is (4/3)/3 or 4/9.

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Tom -> 1 room in 6 hours -> 1/6 room in 1 hour
Peter -> 1 room in 3 hours -> 1/3 room in 1 hour
John -> 1 room in 2 hour -> 1/2 room in 1 hour

Tom and Peter together = 1/2 room in 1 hour
Tom and Peter and John = 1 room in 1 hour

So Tom starts first and paints 1/6 of the room
Then Peter joins in for an hour and they finish up 1/2 of the room. (total 2/3 painted)
Finally John comes along and they finish up the remaining 1/3 of the room. This takes 1/3 of an hour to complete.

SO Peter works 4/3 hours and in this amount of time, he would have painted 4/3*1/3 = 4/9 of a room.

Go with E
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Agree with E. You can also sum the fractions of the job that Peter did complete the job:

When it's Tom + Peter, Peter completes 1/3 of the job
When it's all three of them, Peter completes 1/3 *1/3 of the job or 1/9

1/3 + 1/9 = 1/3 + 3/9 = 4/9
Manager
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Thanks, guys1 OA is E.
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Re: Work Rate [#permalink]  20 Aug 2007, 23:06
abhi_ferrari 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?

1/9
1/6
1/3
7/18
4/9

ughhhh super combined rate problems...

First hour Tom completes 1/6 of the job. so there is 5/6 of the job remaining.
Second hour Tom+Peter 1/6+1/3=3/6 so 3/6 of the job was completed.
2/6 of the job is remaining.
now remaining time Tom+Peter+John =6/6 or 1. using d=rt ->2/6=t1

or t=1/3 of an hour. So Tom Peter and John worked the following hours:
T:2 1/3 hours. P: 1 1/3 hours J: 1/3 hour.

We are looking for the total work done by Peter so again us d=rt. d=1/3*1 1/3 hrs. or d=1/3*4/3 d= 4/9

Ans E.

You can also find out the d for the other two workers. T: d=1/6*7/3 -->7/18

J: d=1/2*1/3= 1/6
Re: Work Rate   [#permalink] 20 Aug 2007, 23:06
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