Earlier work on the size-density hypothesis led to a theory of time-minimization from which the size-density relation could be derived. Subsequently, time-minimization theory was employed to derive expected relations between population and area for cities and urbanized areas, expectations which were empirically confirmed. The present paper derives three well-known and empirically supported relationships from the time-minimization assumption: the gravity model of interaction, the intra-urban density function, and the rank-size rule for cities.