This paper presents an inverse problem for mean field games where we find the mean field problem statement for which the given dynamics is the solution. We use distributed traffic as an example and derive the classic Lighthill Whitham Richards (LWR) model as a solution of the non-viscous mean field game. We also derive the same model by choosing a different problem where we use travel time, which is a distributed parameter, as the cost for the optimal control. We then study the stationary versions of these two problems and provide numerical solutions for the same.