Combining time-dependant structural loading with dynamic crack propagation is a problem that has been under consideration since the early days of fracture mechanics. Here we consider a method to deal with this issue, which combines a set-valued opening-rate-dependant cohesive law, a quasi-explicit solver and the eXtended Finite Element Method of representing a crack. The approach allows a propagating crack to be mesh-independent while also being dynamically informed through a quasi-explicit solver. Several well established experiments on glass (Homolite-100) and Polymethyl methacrylate (PMMA) are successfully modelled and compared against existing analytical solutions and other approaches in 2D up until the experimentally observed branching speeds. The comparison highlights the robustness of ensuring energy is conserved globally by treating a propagating phenomenological crack-tip implicitly, while taking advantage of the computational efficiency of treating the global dynamics explicitly.