Many public transportation systems are unable to keep up with growing passenger demand as the population grows in urban areas. The slow or lack of improvements for public transportation pushes people to use private transportation modes, such as carpooling and ridesharing. However, the occupancy rate of personal vehicles has been dropping in many cities. In this paper, we describe a centralized transit system that integrates public transit and ridesharing, which matches drivers and transit riders such that the riders would result in shorter travel time using both transit and ridesharing. The optimization goal of the system is to assign as many riders to drivers as possible for ridesharing. We give an exact approach and approximation algorithms to achieve the optimization goal. As a case study, we conduct an extensive computational study to show the effectiveness of the transit system for different approximation algorithms, based on the real-world traffic data in Chicago City; the data sets include both public transit and ridesharing trip information. The experiment results show that our system is able to assign more than 60% of riders to drivers, leading to a substantial increase in occupancy rate of personal vehicles and reducing riders' travel time.