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

First Hr : T starts working and in 1 hour can finish 1/6 of the job

Second Hr: T & P starts working and in an hr can finish 1/6+1/3 = 3/6 of the job. So Total 4/6 of the job is finished by now

Third Hr: T,P & J starts working but they have only 2/6 of the job remaining.

Working together they need one hr to finish the entire job (work formula 1/6+1/3+1/2 = 1/1 = 1 hr)

so they work only for 2/6 of an hour.

THerefore peter working at a rate of 1/3 can do only 1/3*2/6 = 1/9 of the job before the job is finished.

Total Job done by Peter = 1/3+1/9 = 4/9

Is there a shorter or quicker way to do it?