Tom, working alone, can paint a room in 12 hours. Peter and John, working independently, can paint the same room in 6 hours and 2 hours, respectively. Tom starts painting the room and works on his own for two hour. He is then joined by Peter and they work together for two 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?  Pick:
A) 5 / 3  B) 1 / 3  C) 7 / 3  D) 4 / 9  E) 3 / 5

Rationale: let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 12 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 6 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 12 * ( t + 4 ) + 1 / 6 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 12 - - > ( t + 4 ) + ( 2 t + 2 ) + 6 t = 12 - - > t = 2 / 3 ; hence peter has done 1 / 6 * ( 2 / 3 + 2 ) = 1 / 6 * 8 / 3 = 8 / 18 = 4 / 9 answer : d
Answer: D