In today's IEEE 802.11 Wireless LANs (WLANs), e.g., the popular IEEE 802.11 b, stations support multiple transmission rates, and use them adaptively depending on the underlying channel condition via link adaptation. It has been known that when some stations use low transmission rates due to bad channel conditions, the performance of the stations using high rates is heavily degraded, and this phenomenon is often referred to as performance anomaly. In this paper, we model the WLAN incorporating stations with multiple transmission rates in order to demonstrate the performance anomaly analytically. Note that all the previously proposed models of the IEEE 802.11 assume a single transmission rate. We also develop possible remedies to improve the performance. Our solution is basically to control the access parameters such as the initial backoff window, the frame size, and the maximum backoff stage, depending on the employed transmission rate. Throughout simulations, we demonstrate that our analytical model is accurate, and the proposed mechanism can indeed provide the remedies to the performance anomaly by increasing the aggregate throughput up to six times.