This paper presents a new accurate mathematical analysis on the performance of distributed cooperative systems employing time-based relay selection protocols. A time-based distributed protocol relates the packets' transmission time to their signal strengths such that the best relay transmits firstly and all other relays abort their transmissions once they sense a busy channel. However, this protocol fails to select the best relay when relay nodes become hidden from each other resulting in self-interferences. In this paper, a new unified mathematical method is developed in order to derive a new exact expression for the average spectral efficiency of the distributed cooperative system in the presence of self-interferences. The developed method accounts for arbitrary fading scenarios and significantly simplifies the difficult task of obtaining the exact average spectral efficiency. Monte Carlo simulations are presented in order to validate the analytical result and to illustrate the impact of hidden nodes on the system performance.