Answer:
E. 4/9
Step-by-step explanation:
Let the time when all three were working together is given by t hours.
Hence,
Tom worked for [tex]t+2[/tex] hours and has done [tex]\frac{1}{6} (t+2)[/tex] part of the job.
Peter worked for [tex]t+1[/tex] hours and has done [tex]\frac{1}{3} (t+1)[/tex] part of the job.
John worked for t hours and has done [tex]\frac{1}{2} (t)[/tex] part of the job.
As they are completing 1 job, we can equate the equation:
[tex]\frac{t+2}{6} +\frac{t+1}{3} +\frac{t}{2} =1[/tex]
=> [tex]\frac{t+2+2t+2+3t}{6}=1[/tex]
=> [tex]\frac{6t+4}{6}=1[/tex]
=> [tex]6t+4=6[/tex]
=> [tex]6t=2[/tex]
=> [tex]t=\frac{2}{6} =\frac{1}{3}[/tex]
Hence, Peter has done [tex]\frac{1}{3} \times(\frac{1}{3} +1)[/tex]
= [tex]\frac{1}{3} \times(\frac{4}{3})[/tex]
= [tex]\frac{4}{9}[/tex]
Hence, option E is the answer.
