Much research has shown that a carefully designed auto rate medium access control can utilize the underlying physical multi-rate capability to exploit the time-variation of the channel. In this paper, we develop a simple analytical model to elucidate the rule that maximizes the throughput of RTS/CTS based multi-rate wireless local area networks. Based on the discovered rule, we propose two distributed fair auto rate medium access control schemes called FARM and FARM+ from the view-point of throughput fairness and time-share fairness, respectively. With the proposed schemes, after receiving a RTS frame, the receiver selectively returns the CTS frame to inform the transmitter the maximum feasible rate probed by the signal-to-noise ratio of the received RTS frame. The key feature of the proposed schemes is that they are capable of maintaining throughput/time-share fairness in asymmetric situation where the distribution of SNR varies with stations. Extensive simulation results show that the proposed schemes outperform the existing throughput/time-share fair auto rate schemes in time-varying channel conditions.