Answer: (m+n)/(mn)
Work Shown:
Josh:
1 room = m hours
1/m room = 1 hour
Kevin:
1 room = n hours
1/n room = 1 hour
We see that the rates for Josh and Kevin are 1/m and 1/n respectively. This is the amount of a room they paint in one hour. Combine the fractions
1/m + 1/n = n/(mn) + m/(mn) = (n+m)/(mn) = (m+n)/(mn)
The expression (m+n)/(mn) represents how much of the room they get painted in 1 hour. This is if they work together and it assumes neither worker slows the other one down.
