We study a simple model for traffic flow on networks based on the LWR model. We consider a system of conservation laws with space-dependent and discontinuous flux, each of which describes the evolution of a population of drivers with a unique origin-destination pair. The main advantage of this formulation is that junctions actually disappear, so that a unique mathematical theory can be applied for the whole network, i.e., there is no need to manage junctions separately as in the classical theory. Surprisingly, if the equations are numerically approximated by means of the Godunov scheme, the resulting algorithm automatically maximizes the flux at junctions, thus respecting the typical assumptions of the classical theory. Numerical examples for small- and medium-scale networks are provided, aiming at showing the simplicity of the algorithm.