Problem Solving

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

The OA is E. Can anyone explain?

The key to this question is to choose a number that you can use to denote the total amount of work.

I'm going with 18 since that is the highest number that in the answers and is divisible by 6,2,and 3

So there are 18 total units of work

Tom can finish 18 units in 6 hrs.. So he works at a rate of 3 units/hr

Peter finishes in 3 hrs .. = 6 units/hr

John finishes in 2 hrs = 9 units/hr

Now let's go on an hour by hour basis.

Hr 1 | 3 units of work done (Tom works alone)
Hr 2 | 3 + 6 units of work done (Tom + Peter)

Now at the end of hr 2 we have 12 units of work done in total.

18-12 = 6 units of work...

6 units of work will be distributed among Tom, Peter and John.

If you compare their rates of work.

T:P:J = 3:6:9 ... Peter will do 6/18th or 1/3 of the remaining 6 units = 2 units

Total work that Peter does = 6 (from hr 2) + 2 (from hr 3) = 8

So peter does 8 units out of 18 ... = 8/18 = 4/9

This is an easy problem if you choose the right number... Otherwise you will spend ages trying to figure out the answer!