The volume of a pyramid is given by the formula:
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
The volume of a rectangular prism is given by the formula:
\[ V_{\text{prism}} = \text{Base Area} \times \text{Height} \]
Since the prism and the pyramid have congruent bases and equal heights, we can establish that:
\[ V_{\text{prism}} = 3 \times V_{\text{pyramid}} \]
Given that the volume of the pyramid is 48 in³:
\[ V_{\text{prism}} = 3 \times 48 \text{ in}^3 = 144 \text{ in}^3 \]
Thus, the volume of the prism is \( 144 \text{ in}^3 \).