What are the results of collisions between faster-moving particles and slower-moving particles?
The faster-moving particles have higher kinetic energy. Energy flows from high to low, thus uniformizing the energy distribution amongst the particles.
So, the slower-moving particles end up moving a bit faster, and the faster-moving particles end up moving a bit slower.
Assuming that they are ideal particles that conserve kinetic energy, they would all approach the same average kinetic energy and thus the same temperature and root-mean-square speed.