We report on experimental and theoretical results on the dynamical behavior of propagating solitary relaxations in a model system for earthquake-like dynamics. In the experiments, a continuous elastic medium is sheared at very slow rate in between two coaxial cylinders. Solitary propagating relaxations travel at speeds that are proportional to the driving speed, though ∼ 10³ times faster, and inversely proportional to the number of solitary relaxations in the system. We show that this behavior appears due to the existence of a characteristic length scale which is the typical displacement of a surface element in a relaxation.