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We consider a multi-hop, ad hoc network using the IEEE 802.11b technology, where the nodes may employ different transmission rates depending on their channel conditions. It has been observed that such a network scenario poses new challenges concerning traffic routing as well as channel access. In this paper, we propose a novel scheme for route selection that, by using cross-layer interactions, yields improved throughput performance. Whenever a source node requires a route to reach a destination node, the proposed scheme determines the best source-destination path based on the following MAC parameters: the collision probability and the available bandwidth. Thus, by exploiting the synergy between network layer and MAC layer, the route providing the highest throughput is selected. Results obtained through the ns-2 simulator show the effectiveness of the proposed approach.