Question 202013
Let's first find the hourly rate of each painter:
If Ben can paint the entire house in 36 hours, then he can paint {{{1/36}}} of the house in 1 hour.
If Carlos can paint the entire house in 24 hours, then he can paint {{{1/24}}} of the house in 1 hour.
Working together, Ben & Carlos can paint {{{(1/36)+(1/24) = 5/72}}} of the house in 1 hour.
In 12 hours they can paint {{{(12)*(5/72) = 5/6}}} of the house, which leaves only {{{1/6}}} of the house to finish.
Now the question, how long will it take Carlos to finish the house?
Well, Carlos can do {{{1/24}}} in 1 hour, so you can let x = the number of hours Carlos needs and form a proportion:
{{{1/6 = x/24}}} Multiply the first fraction by {{{4/4}}} to get the common denominator of 24.
{{{(4/4)*(1/6) = x/24}}} Evaluate.
{{{4/24 = x/24}}} so...
{{{x = 4}}}
Carlos needs 4 hours to finish the job.