Question 813210
Their rates are added simply if they work simultaneously (or at least, that is the idea to use).


The painter:  1/8 jobs per hour
The assistant:  1/10 jobs per hour
Both together:  {{{1/8+1/10=5/40+4/40=highlight(9/40)}}}


That is NINE jobs per FORTY hours.  You want the time h in hours for both people to do 1 job.  


{{{highlight((9/40)*h=1)}}}
{{{h=40/9=highlight(4&4/9)}}} hours