Question 818894
Each of them might work according to his stated, given work speed.  The work speeds are additive.


Use the speeds (rates) in the form of roofs per day.
Homeowner rate plus roofer rate equals their combined rate:
{{{(1/7)+(1/2)=2/14+7/14=highlight(9/14)}}} roofs per day, like 9 roofs in 14 days.


You are interested in the reciprocal, {{{14/9=highlight(1&5/9)}}} day for 1 roof.
A more realistic interpretation requires a little more information about how many hours per day is given for any day's work.