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?
ughhhh super combined rate problems...
First hour Tom completes 1/6 of the job. so there is 5/6 of the job remaining.
Second hour Tom+Peter 1/6+1/3=3/6 so 3/6 of the job was completed.
2/6 of the job is remaining.
now remaining time Tom+Peter+John =6/6 or 1. using d=rt ->2/6=t1
or t=1/3 of an hour. So Tom Peter and John worked the following hours:
T:2 1/3 hours. P: 1 1/3 hours J: 1/3 hour.
We are looking for the total work done by Peter so again us d=rt. d=1/3*1 1/3 hrs. or d=1/3*4/3 d= 4/9
You can also find out the d for the other two workers. T: d=1/6*7/3 -->7/18
J: d=1/2*1/3= 1/6