Let's use the formula:
$$\frac{1}{t_{1}} + \frac{1}{t_{2}} = \frac{1}{t}$$
where $t_1$ is the time it takes for the hot water faucet to fill the tub, $t_2$ is the time it takes for the cold water faucet to fill the tub, and $t$ is the time it takes for both faucets to fill the tub together.
Substituting the given values, we have:
$$\frac{1}{13} + \frac{1}{12} = \frac{1}{t}$$
Simplifying the left side:
$$\frac{12 + 13}{12 \cdot 13} = \frac{1}{t}$$
$$\frac{25}{156} = \frac{1}{t}$$
Cross-multiplying:
$$25t = 156$$
Dividing by 25:
$$t = \frac{156}{25} \approx 6.24$$
Therefore, it will take about 6.24 minutes or approximately 6 minutes and 14 seconds to fill the tub if both faucets are used together.