Question

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. 1/9B. 1/6C. 1/3D. 7/18E. 4/9

Answer 1

E. 4/9

Explanation:

Let the time when all three were working together is given by t hours.

Hence,

Tom worked for
`t+2` hours and has done
`(1)/(6) (t+2)` part of the job.

Peter worked for
`t+1` hours and has done
`(1)/(3) (t+1)` part of the job.

John worked for t hours and has done
`(1)/(2) (t)` part of the job.

As they are completing 1 job, we can equate the equation:

`(t+2)/(6) +(t+1)/(3) +(t)/(2) =1`

=>
`(t+2+2t+2+3t)/(6)=1`

=>
`(6t+4)/(6)=1`

=>
`6t+4=6`

=>
`6t=2`

=>
`t=(2)/(6) =(1)/(3)`

Hence, Peter has done
`(1)/(3) *((1)/(3) +1)`

=
`(1)/(3) *((4)/(3))`

=
`(4)/(9)`

Hence, option E is the answer.