Opportunistic routing has recently been proposed for ad hoc networks. Several works showed that opportunistic routing improves network performance. None of these works, however, studied the integration of opportunistic routing into multi-rate ad hoc networks. In this paper, we study this integration. Specifically, we consider the problem of determining the required number of retransmissions in opportunistic routing and the transmission rate in each retransmission such that the required (re)transmission time for a sent packet is minimized while at the same time a target end-to-end PER is satisfied. We show that this problem is NP-hard. Accordingly, we propose an approximate solution called Opportunistic routing Over Multi-rate Multi-hop ad hoc networks (OOMM). Extensive simulations over a multi-rate OFDM-based UWB network show that OOMM achieves high performance relative to different routing techniques (21%-48% throughput improvement).