The present paper is devoted to travel time equilibration procedure for solving traffic assignment problem with respect to route flows. We prove that equilibrium route-flow assignment can be easily obtained by implementing equilibration procedure together with simple rules for sequential extension and/or by reducing the set of active routes. Accurate route-flow solution for the small Sioux Falls network is found via the developed algorithm and demonstrates some important points related with visualization issues, decision making support and scenario analysis in the sphere of transportation planning.