If Nita can paint the room in 3 hours, she gets 1/3 of the room done in an hour; likewise, is Jorge can paint the room in 4 hours, he gets 1/4 of the room done in an hour. We are asked how long it takes for them when they combine their efforts, so we add their times together, hours on the bottom of the fractions, and set it equal to 1/x, x being the number of hours they get the job done together (hours also on the bottom to keep the equation proportionate). [tex] \frac{1}{4}+\frac{1}{3}=\frac{1}{x} [/tex]. In order to add those we have to find a common denominator, which happens to be 12. [tex] \frac{3}{12}+\frac{4}{12}=\frac{1}{x} [/tex], and [tex] \frac{7}{12}=\frac{1}{x} [/tex]. Cross multiply to get 7x = 12. Divide both sides by 7 to find that it takes them 1.71 hours to paint the room together (a little over an hour and a half).
