The Traveling Car Renter Problem (CaRS) is a generalization of the classic Traveling Salesman Problem (TSP), where the tour of visits can be broken down into contiguous paths that can be traveled with different rental cars. The objective is to determine the Hamiltonian circuit that has a final minimum cost, considering the penalty paid for each vehicle change on tour. The penalty is the cost of returning the car to the city where it was rented. CaRS is classified as an NP-hard problem. The research focuses on hybrid procedures that combine meta-heuristics and methods based on Linear Programming to deal with CaRS. The hybridized algorithms are scientific algorithms (ScA), variable neighborhood descent (VND), adaptive local search procedure (ALSP), and a new ALSP variant called iterative adaptive local search procedure (IALSP). The following techniques are proposed to deal with the CaRS: ScA+ALSP, ScA+IALSP, and ScA+VND+IALSP. A mixed integer programming model is proposed for the CaRS, which is used in ALSP and IALSP. Nonparametric tests are used to compare the algorithms in a set of instances in the literature.