Pump machine 1 & 2

Let the volume of the swimming pool be $V$ . Then the pumping rates of pump $A$ and pump $B$ are $\dfrac V6$ per hour and $\dfrac V4$ per hour respectively. If the time taken for the two pumps to fill the swimming pool is $t$ hours, then:

$\begin{aligned} \left(\frac V6 + \frac V4\right)t & = V \\ \left(\frac 16 + \frac 14\right)t & = 1 \\ \frac {10}{24}t & = 1 \\ \implies t & = \boxed{\text{2.4 hours}} \end{aligned}$

In one hour, pump $A$ will fill $\frac{1}{6}$ of a pool and pump $B$ will fill $\frac{1}{4}$ .

Between them, they fill $\frac16+\frac14=\frac{5}{12}$ of a pool in one hour. It therefore takes $\frac{12}{5}=\boxed{2.4}$ hours to fill a pool with both pumps working together.