The IEEE 802.11 standard supports multiple PHY rates. However, the IEEE 802.11 DCF in a multiple-rate environment may cause a performance anomaly. There have been many studies about the performance analysis and improvement of single- and multi-rate WLAN systems. However, there were a few studies about a generalized analysis on throughput and channel utilization for successful transmissions in multi-rate WLAN systems with different frame parameters and channel errors. In particular, the performance anomaly problem of the multi-rate WLANs still needs to be solved. We propose a more generalized mathematical model for each station with a different data transmission time and mathematically analyze the throughput and channel utilization for successful transmission in error-prone multi-rate WLANs. Moreover, we propose a contention window size adjustment scheme and a payload adjustment scheme to resolve the well-known performance anomaly problem in multirate WLANs by achieving temporal fairness. Numerical results show that the proposed scheme is very effective in achieving temporal fairness.