The growing global Internet traffic will inevitably lead to a serious upgrade of the current optical networks' capacity. Instead of upgrading the data rate of each wavelength in every fibre link across the entire optical WDM network infrastructure, it is more efficient and cost-effective to support different data rates within one fibre link (e.g., 10, 40 and 100 Gbps). This is called optical network with mixed line rates (MLR). Moving to higher than 10Gbps data rates that can be used within the same fibre requires the implementation of phase modulation schemes. Nevertheless, the co-existing OOK channels cause a critical physical impairment to the phase modulated channels, namely cross-phase modulation (XPM), that limits the network's performance. In order to mitigate this type of impairment a more sophisticated physical impairment aware routing and wavelength assignment scheme needs to be adopted. In this paper, the critical impairment for each data rate and the way it affects quality of transmission (QoT) is presented. Secondly, a novel dynamic RWA algorithm for a MLR optical network is proposed in order to address this issue. Finally, our proposed method is compared through simulations with the shortest path and minimum hop routing schemes.