Carpooling is an efficient measure to fight car ownership and reduce vehicle kilometres travelled. By individuals sharing their commutes, vehicle occupancy increases and congestion is reduced. We develop a dynamic ADL (Arnott, de Palma, Lindsey)-Vickrey approach for a corridor monocentric city a la Hotelling. First, we formulate the matching problem of heterogeneous users in carpooling as an MILP problem and we discuss its analytical properties when there is no congestion. Next, we construct a bi-level optimization problem involving matching (first stage) and dynamic traffic congestion with scheduling preferences (second stage) when congestion is endogenous. We provide a heuristic to attain an optimal matching for a dynamic traffic equilibrium with congestion. Such a template allows studying the two-way causality between dynamic congestion and carpooling matching.