The average relative speed of gas molecules is a core physical quantity for understanding the transport properties of gases. This work derives expressions for the average relative speed of ideal gases under three common statistical distributions—Boltzmann, Fermi, and Bose distributions. For the Boltzmann distribution, corresponding to Maxwell distribution, the analytical solution of the average relative speed is rigorously derived. At absolute zero temperature, the average relative speed and average speed of an ideal Fermi gas are u=3635vF and v=34vF (vF is the Fermi rate), respectively, while both the average relative speed and average speed of an ideal Bose gas are zero. At non-zero temperatures, these quantities need to be solved via numerical integration. Calculation results show that the average relative speed and average speed are entirely determined by the velocity distribution law, which provides an important supplement to thermal physics teaching related to the kinetic theory of gases.