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Tom, working alone, can paint a room in 6 hours. Peter and [#permalink]
12 Oct 2008, 19:08

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

I have not been able to crack this one within 5 min..Can you guys help me ???

Re: Working together !! [#permalink]
12 Oct 2008, 19:39

kishankolli 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

I have not been able to crack this one within 5 min..Can you guys help me ???

first hour 1/6 of work is done second hour peter has done 1/3 (his rate) times 5/6 (the job remaining) =5/18 third hour peter has done 1/3 times 1/3 of work remaining =2/9

solution 7/18

this types of problems r usually solved by formula so that kinda drives the attention out from the convenient approach

if i got this right tho.. _________________

The one who flies is worthy. The one who is worthy flies. The one who doesn't fly isn't worthy

Re: Working together !! [#permalink]
12 Oct 2008, 20:14

Please let me knoe if I am doing anything wrong here:

In the first 1 hr, Tom covered = 1/6R In the second hr, Tom and Peter coverd = 1/6R + 1/3R So in two hrs, they combinedly covered = 2/3R which leaves, only 1/3R to be covered. Now all of them joined and completed the work in the next X hrs => X/6R + X/3R + X/2R = R/3 => X = 1/3 Hrs

So in 1/3rd hour John should have painted the fraction of (1/3)(1/2R) = R/6

Re: Working together !! [#permalink]
12 Oct 2008, 22:07

amitdgr wrote:

leonidas wrote:

(1/3)*(5/6) + (1/3)*(2/6) = 7/18

1st hr = 1/6 of work done. Remaining work = 5/6. Peter does (1/3)*(5/6) =5/18 of the work ----(1)

2nd hr = 1/6 + 1/3 = 3/6 of work is done => In two hrs (1/6+3/6)= 4/6 work is done Remaining work = 1-(4/6) = 2/6

Peter does 1/3* 2/6 = 2/18 of total work. ...(2)

(1) + (2) = 7/18

leonidas... why are we calculating remaining work here ?

We have to know Peter's contribution in the last leg. By calculating the total work in the first 2 hours, remaining work can be calculated and hence peter's contribution in the last leg (i.e remaining work after 2 hours). Did I confuse you? _________________

To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton

Re: Working together !! [#permalink]
12 Oct 2008, 22:47

smahamkl wrote:

Please let me knoe if I am doing anything wrong here:

In the first 1 hr, Tom covered = 1/6R In the second hr, Tom and Peter coverd = 1/6R + 1/3R So in two hrs, they combinedly covered = 2/3R which leaves, only 1/3R to be covered. Now all of them joined and completed the work in the next X hrs => X/6R + X/3R + X/2R = R/3 => X = 1/3 Hrs

So in 1/3rd hour John should have painted the fraction of (1/3)(1/2R) = R/6

Question is asking for Peter....hence it will be (1/3)*(R/6) = R/18.

Hence, total work done by peter = R(1/6 + 1/6 + 1/18) = 7R/18.

Re: Working together !! [#permalink]
13 Oct 2008, 00:20

I made a mistake on (1) Remaining work = 5/6. Peter does (1/3)*(5/6) =5/18 of the work ----(1)

Here I am double counting P's work

1/6 + (1/6 + 1/3) = 4/6 is done...i.e 1/3 is remaining aftre hr 2 now 3 of them who work in the ratio of 1/6:1/3:1/2 will work on the remaining work which is 1/3 of total work so P worked: 1/3 + .33/(.167+.334+0.5)*1/3 : 1/3 + 1/9 = 4/9

I make so many mistakes _________________

To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton

Re: Working together !! [#permalink]
13 Oct 2008, 02:06

Tom's individual rate is 1 job / 6 hours or 1/6 job/hr ("job per hour"). During the hour that Tom works alone, he completes 1/6 of the job, using rt = w: (1/6 job/hr) x 1 hr = 1/6 job.

Peter's individual rate is 1 job / 3 hours or 1/3 job/hr. Peter joins Tom and they work together for another hour; Peter and Tom's respective individual rates can be added together to calculate their combined rate: 1/6 + 1/3 = 1/2 job/hr. Working together then they will complete 1/2 of the job in the 1 hour they work together.

At this point, 2/3 of the job has been completed (1/6 by Peter alone + 1/2 by Peter and Tom), and 1/3 remains.

When John joins Tom and Peter, the new combined rate for all three is: 1/6 + 1/3 + 1/2 = 1 job/hr. The time that it will take them to finish the remaining 1/3 of the job can be solved: rt = w -> (1 job/hr)(t) = 1/3 job -> t = 1/3 hr.

The question asks us for the fraction of the job that Peter completed. In the hour that Peter worked with Tom he alone completed: rt = w -> w = (1/3 job/hr) x (1 hr) = 1/3 of the job.

In the last 1/3 of an hour that all three worked together, Peter alone completed: (1/3 job/hr) x (1/3 hr) = 1/9 of the job. Adding these two values together, we get 1/3 job + 1/9 job = 4/9 of the job.