Question 629240
What is the given rate of work of each person working alone?

1:  Tim would work 20 hours to paint one house alone.
h = number of houses; w = actual work hours; 20 is the hours per house
20 times h equals w  or  
{{{20h = w}}}

2:  Friend of Tim, would work 30 hours to paint one house alone.
h = number of houses; w = actual work hours; 30 is the hours per house
30 times h equals w or
{{{30h = w}}}

3:  20h = w and 30h = w .......... w square = 20h * 30h = 600
{{{w^2 = 600h^2 = 600}}} (h = 1, & the square of h = 1)

Solve:  {{{sqrt(600) = w = 24.49}}} actual work hours -combined- (that is two people). Divide by the number of workers, i.e. divide by 2. 
{{{24.49/2 = 12.25}}}

Answer:  Working together the house is done in 12 and a quarter hours; 12 hours 15 minutes.