Question

i need help with this yall
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.

Answer 1

general approach is to write an expression for the portion of the whole job that each component does per unit of time

put more simply:

let's say the large pump by itself can fill the whole pool in L hours. therefore each hour it does (1/L) portion of the whole pool.

and the small pump by itself can fill the whole pool in S hours. same logic, each hour it fills (1/S) of the whole pool.

so 2 large pumps together fill 2*(1/L) of the pool per hour. one small pump fills (1/S) of the pool per hour. as the problem states, 2 large and 1 small fill the pool in 4 hours. so after one hour only, they've done 1/4 of the whole job.

writing the equation: 2(1/L) + (1/S) = 1/4

Answer 2

you also know that one large and 3 small pumps can also fill the same swimming pool in 4 hours, so you can write a second equation for this. once you have both equations, you can solve the system for L and S.

finally, to find the time it'll take for 4 large and 4 small pumps to fill the pool, these pumps will fill 4(1/L) + 4(1/S) of the pool per hour using our previous logic. plug in the L and S values. you'll end up with the fraction of the pool filled in *one* hour. to find the number of hours it takes to fill the whole pool, simply calculate 1 / (that fraction).