+15 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.)
+128474 Call the portion of the job that the large pump can do in 1 hour = 1/R where R is the total number of hours that it takes 1 large pump to complete the task
Call the portion of the job that the small pump can do in 1 hour = 1 / r where r is the total number of hours that it takes 1 small pump to complete the task
And Rate x Time = Amt of the job done
So...we have the following system
2*(1/R)*4 + 1*(1/r)*4 = 1 → 8/R + 4/r = 1
1*(1/R)*4 + 3*(1/r)*4 = 1 → 4/R + 12/r = 1
Multiply the second equation by -2 and add it to the first
-20/r = -1 → r/20 = 1 so r = 20 hours for one small pump to fill the pool
And using 8/R + 4/r = 1 to solve for R, we have
8/R + 4/20 = 1
8/R + 1/5 = 1
8/R = 4/5
R/8 = 5/4
R = 40/4 = 10 hrs for one large pump to fill the pool
So... for 4 large pumps and 4 small pumps working in unison, we have.....
The 4 large pumps will fill 4/10 = 2/5 of the pool in one hour [each fills 1/10 of the pool in one hour]
The 4 small pumps will fill 4/20 = 1/5 of the pool in one hour [each fills 1/20 of the pool in one hour]
So...in one hour 2/5 + 1/5 = 3/5 of the pool is filled
And...inverting this fraction gives us the total time = 5/3 hrs = 1 + 2/3 hrs = 1 hr 40 min
