We compare the azimuthal correlations arising from three and two hadron production in p+p and Au+Au collisions at sq.rt.(S(NN))=200 GeV. We show that in Au+Au, the two away side partons in two-to-three processes have in average a smaller and a greater path length than the average path length of the away-side parton in two-to-two processes. Since in average the particle with the shortest path length in two-to-three processes loses less energy, with respect to the away-side particle in two-to-two processes, this effect leads to a relative enhancement of the ratio of two-to-three to two-to-two processes in Au+Au compared to p+p collisions. We argue that this phenomenon may be responsible for the shape of the away side in azimuthal correlations at the Relativistic Heavy-Ion Collider.