Assume that Tom, Peter and John have worked for x hours to finish the remaining work.
This implies that Tom worked for 2+x hours, Peter worked for 1+x hours and John worked for x hours to complete the work.

So 1/6 * (2+x) + 1/3 * (1+x) + 1/2 * x = 1 (the sum of fractions of work completed by the 3 is equal to the entire work)

Solving for x, x = 1/3

Hence the fraction of work x
Tom completed is 1/6 * (2 + 1/3) = 1/6 * 7/3 = 7/18
Peter completed is 1/3 * (1 + 1/3) = 1/3 * 4/3 = 4/9
John completed is 1/2 * 1/3 = 1/6

Hence the answer is 4/9.

BRILLIANT EXPLANATION. THANKS SO MUCH! BEST OF LUCK FOR YOUR GMAT!

rb90 wrote:BRILLIANT EXPLANATION. THANKS SO MUCH! BEST OF LUCK FOR YOUR GMAT!

Thanks!!!

rb90 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?

(A)1/9
(B)1/6
(C)1/3
(D)7/18
(E)4/9

Please explain the working. OA is E

Another approach would be to plug in a value for the room. Let room = 54.

Rate for T = 54/6 = 9/hr.
Rate for P = 54/3 = 18/hr.
Rate for J = 54/2 = 27/hr.

T works for 1 hour = 9*1 = 9.
Remaining work = 54-9 = 45.

T works for 1 hour = 9*1 = 9.
P works for 1 hour = 18*1 = 18.
Remaining work = 45-9-18 = 18.

Combined rate for T+P+J = 9+18+27 = 54/hr.
Time for T+P+J to finish = 18/54 = 1/3 of an hour.
Work done by P = 18 * 1/3 = 6.

Total work for P = 18+6 = 24.
Fraction of work by P = 24/54 = 4/9.

The correct answer is E.