Averaging is a valuable technique to gain understanding of the long-term evolution of dynamical systems characterized by slow dynamics and fast periodic or quasi-periodic dynamics. The authors recently proved that averaging can be applied to the extremal flow of optimal control problems with one fast variable, with a special treatment of the adjoint of this fast variable. The present work extends these results by tackling averaging of time optimal systems with two fast variables, that is considerably more complex because of resonances. No general theory is presented, but rather a thorough treatement of an example, based on numerical experiments. After providing a justification of the possibility to use averaging techniques for this problem ``away form resonances'' and discussing compatibility conditions between adjoint variables of the original and averaged systems, we analyze numerically the impact of resonance crossings on the dynamics of adjoint variables. Resonant averaged forms are used to model the effect of resonances and cross them without loosing the accuracy of the averaging prediction.