Real-time ridesharing systems have been investigated as a potential method for improving congestions in overloaded road networks. In this paper, we specifically investigate integrating dynamic road conditions (DRCs) such as traffic accidents into the ridesharing systems, as the DRCs will cause unexpected delays during the route planning phase. We propose to use the CRP framework due to its capability of handling frequent road edge updates, and we will discuss the relevant issues on traffic data preprocessing, time conflict detection on ridesharing schedules, and the importance of utilizing a probability traffic model based on historical data. Our preliminary experiments show the impressive efficiency of CRP on DRC updates of varying batch sizes and distributions.