Question 860083
The rate of the painter and his apprentice working simultaneously is the sum of their individual rates.


Painter, 1/u jobs per hour
Apprentice, 1/(u+5) jobs per hour
Painter + Apprentice, 1/12 jobs per hour
The variable, u, is assigned as the time for the painter to paint the one house.


{{{highlight_green(1/u+1/(u+5)=1/12)}}}.
That was the analysis leading to the equation.


Solve the the single variable equation for  u.  Use it to compute u+5.