This paper proposes a tractable model for the design of a rapid transit system. Travel cost is minimized and traffic capture is maximized. The problem is modeled on an undirected graph and cast as an integer linear program. The idea is to build segments within broad corridors to connect some vertex sets. These segments can then be assembled into lines, at a later stage. The model is solved by branch-and-cut within the CPLEX framework. Tests conducted on data from Concepción, Chile, confirm the effectiveness of the proposed methodology.