Each good worker can paint my new house alone in 12 hours. each bad worker can paint my house alone in 36 hours. i need my house painted in 3 hours. if i can only find 3 good workers, how many bad workers must i also find in order to have my house painted on time?

In 3 hours, one good worker can paint one fourth of your house. Three good workers can thus paint three fourths of your house in three hours, leaving one fourth to be done by bad workers.

One bad worker can paint one twelfth of your house in 3 hours. There are three twelfths in one fourth, so you will need to hire three bad workers to have your house painted on time.