## Problem Statement:

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.)

## Solution:

Let R and r be the rate of work of the large and the small pumps respectively.

So, 4(2R + r) = 1. [2 large and 1 small pump work for 4 hours to do 1 job.]

And, 4(R + 3r) =1 [1 large and 3 small pumps 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.