  In this paper we study a facility location problem in the plane in which a
single point (facility) and a rapid transit line (highway) are simultaneously
located in order to minimize the total travel time of the clients to the
facility, using the $L_1$ or Manhattan metric. The rapid transit line is
represented by a line segment with fixed length and arbitrary orientation. The
highway is an alternative transportation system that can be used by the clients
to reduce their travel time to the facility. This problem was introduced by
Espejo and Ch\'ia in [7]. They gave both a characterization of the optimal
solutions and an algorithm running in $O(n^3\log n)$ time, where $n$ represents
the number of clients. In this paper we show that the Espejo and Ch\'ia's
algorithm does not always work correctly. At the same time, we provide a proper
characterization of the solutions with a simpler proof and give an algorithm
solving the problem in $O(n^3)$ time.
