Question 353154
Rate*Time=Output
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Let {{{Z}}} be the number of worker-days to do the work. 
For John,
{{{R[j]*8=Z}}}
{{{R[j]=Z/8}}}
For Peter,
{{{R[p]*6=Z}}}
{{{R[p]=Z/6}}}
When they work together for 2 days,
{{{(R[p]+R[j])*2=(Z/8+Z/6)2=Z/4+Z/3=(3Z)/12+(4Z)/12=(7Z)/12}}}
The work that remains is,
{{{Z-(7Z)/12=(5Z)/12}}}
Find the time it takes John to finish it,

{{{R[j]*t=(5Z)/12}}}
{{{(Z/8)*t=(5Z)/12}}}
{{{t=40/12}}}
{{{highlight(t=10/3)}}}days