1 Two large and 1 small pumps can fill a swimming pool in 4 hours

1 Two large and 1 small pumps can fill a swimming pool in 4 hours

1 Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool.(We assume that all large pumps are similar and all small pumps are also similar.)

Answer：Let R and r the rate of work of the large and the small pumps respectively
4(2R + r) = 1 : 2 large and 1 small work for 4 hours to do 1 job
4(R + 3r) = 1 : 1 large and 3 small work for 4 hours to do 1 job
T(4R + 4r) = 1 : Find time T if 4 large and 4 small are to do one job.
Solve for R and r the system of first two equations then substitute in the third and solve for T to find the time. T = 5/3 hours = 1 hour 40 minutes.