Question

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 1

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.

Answer 2

2L+IS='/4

IL +3S=1 / 4

solving we get

L='/5 and S = I/20

we have to get4L+4s

4x1/5 +4x1/20=4/5+I/5=5/5=l

Ans: I hr