In this paper, we investigate the performance of link adaptation (LA) algorithms for cooperative multiple access multiple relay networks. In the first transmission phase, the sources transmit in turn in consecutive time slots. In the second cooperative retransmission phase, the destination schedules one relaying node to send redundancies. LA is a fundamental mechanism allowing the source nodes to adapt to the radio channel conditions. In this paper, we investigate the problem of rate allocation using a centralized method, where the destination is the central node that determines the source rates. Furthermore, and in sharp contrast with existing cooperative transmission schemes, we consider the packet size to be time-varying. In other words, we propose adapting the slot duration of each of the sources during the transmission phase as a new degree of freedom. Accordingly, the LA process determines the rate and the time slot duration of each source. We consider a practical performance metric namely, the network spectral efficiency. This metric being difficult to be optimized (given the complex multi-variable optimization problem), we propose best-response dynamic (BRD) algorithms to solve the rate and time duration allocation. Then, we conduct a thorough performance analysis using Monte-Carlo simulations. Our numerical results validate the effectiveness of the proposed BRD algorithms as they yield performance close to the corresponding exhaustive search approach. Furthermore, the results ensure the gain of exploiting the new degree of freedom of the variable slot duration.