Tom, John and Peter working together

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ace_gre: Senior | Next Rank: 100 Posts; Posts: 98; Joined: Mon Nov 23, 2009 2:30 pm; Thanked: 26 times; Followed by:1 members

Tom, John and Peter working together

by ace_gre » Mon Jan 25, 2010 9:37 pm

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?

sorry I do not have the answer choices nor the OA. But I tried solving this and reached [spoiler]4/9[/spoiler]
Please provide your answers. Thanks!

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Source: Beat The GMAT — Problem Solving | Mon Jan 25, 2010 9:37 pm

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Mon Jan 25, 2010 9:55 pm

even i am also getting [spoiler]4/9[/spoiler]

tom in 1 hr does 1/6
peter in 1 hr does 1/3
and jhon 1/2

tom and peter=1/2
after two hr tot job done =1/6+1/2=2/3
rest 1/3 job is done by the team

peter does 1/3 of the job whele working with tom
and 1/9 while working with the team
tot=1/9+1/3=4/9

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Tue Jan 26, 2010 1:13 am

ace_gre 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?

sorry I do not have the answer choices nor the OA. But I tried solving this and reached [spoiler]4/9[/spoiler]
Please provide your answers. Thanks!

Say, The total amount of work required to Paint the Room is R, Tom's Rate of painting T, Peter's P and John' J

6T = R; 2J = R ; 3P =R

in one hour Tom finishes 1/6 of the room, Tom and Peter joined together can finish painting (1/6+1/3 ) = 1/2 in one hour

Now what is left is 1/3 of the room to paint (1/6 of which will be done by Tom,2/6 by Peter and 3/6 by John)

Now in the end, what peter did is = 1/3+1/3*3 = 4/9

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