Eight workers from Company A can paint 7 homes in 84 hours. Working together, three workers from Company A and five workers from company B can paint 9 homes in 96 hours. If each worker from company A works at one constant rate, each worker from Company B works at another constant rate, and each home requires the same amount of work to paint, how many workers from Company B are required to paint 9 homes in 60 hours? (A)12 (B)15 (C)18 (D)20 (E)30

Let work perhour of a worker of A be a Total manhours from A = 84*8a = 672a. So 672a hours needed for 7 homes. Let work per hour of B be b (3a+5b)*96 hours are needed for 9 homes. =288a+480b hours are needed for 9 homes. Here, 288*7/672 homes can be built by 3a workers. = 3 homes. Therefore 480b hours are needed for bulding 6 homes by B workers. multiply by 1.5 720b hours are needed for bulding 9 homes. Let the number of workers needed be X Xb*60 hours are needed for 9 homes. xb*60=720b x=12 pick A. What is OA?

Let A be the work productivity for a worker in company A and B for that of company B. 8A can paint 7 homes in 84 hours. 8A=7/84 A=1/96 meaning one worker at company A can finish painting 1/96 of the house per hour. 3A+5B can paint 9 homes in 96 hours. Substituting A=1/96 to this equation, 3(1/96)+5B=9/96 B=1/80 meaning one worker at company B can finish painting 1/80 of the house per hour. So in 60 hours, one worker from company B can paint 60*(1/80)=3/4 of the house. So to paint 9 homes, you need 9/(3/4)=12 workers