Pumping away

Define the following variables:

Rate of water flow in large pump = $x$

Rate of water flow in small pump = $y$

Volume of swimming pool = $V$

Now, we know that

$\text{Volume = Rate of water flow in pumps} \times \text{Time taken}$

For the first statement:

$V = (2x + y) \times 4\implies$ Eq.(1)

For the second statement:

$V= (x+3y) \times 4\implies$ Eq.(2)

Substitute Eq.(1) into Eq.(2):

$(2x+y) \times 4 = (x+3y) \times 4\\ 2x+y=x+3y$

$x=2y\implies$ Eq.(3)

Now, we define $t$ as the time taken for $4$ large and $4$ small pumps to fill the pool. This gives:

$V=(4x+4y) \times t$

Substitute Eq.(1):

$(2x+y) \times 4 = (4x+4y)\times t$

Substitute Eq.(3):

$(2(2y)+y) \times 4 = (4(2y)+4y) \times t\\ 4(5y) = t(12y)\\ t=\dfrac{20y}{12y} = \dfrac{5}{3} \text{ hours} = \dfrac{5}{3} \times 60 = \boxed{100} \text{ minutes}$