A numerical solution to a simple continuum model for traffic flow is discussed. Real traffic data are used for an in-depth study and the implementation of a finite difference scheme is described in detail. The results show that predicted traffic flow conditions agree well with the observed data provided boundary conditions are treated properly. This modelling exercise provides an excellent example of applying mathematics to a fairly complex real life problem. It serves to provide insight into the processes involved in deterministic modelling using a realistic and relevant example.