Conventional theory for homogeneous aquifers states that pressure propagates more rapidly into aquifers than solutes following river stage rise. We demonstrate through numerical simulations of two-dimensional aquifer slices that the relative timing of pressure and solute responses in alluvial aquifers is a function of subsurface structures. Two generic conceptual models of heterogeneity are investigated, a vertical clogging layer and a horizontal sand string. Independent of the conceptual model, the hydraulic conductivity contrast is the primary controlling variable on the rates of pressure and solute transport from a river to an observation point. Conceptual models are compared using metrics for pressure and solute travel time that represent propagation of 50% change in each variable from river to observation point. While not possible in a homogeneous system, a solute travel time less than a pressure travel time can occur in the presence of both types of heterogeneity, and indicates that heterogeneity is controlling propagation from the river to the aquifer. Less than one order of magnitude contrast in hydraulic conductivities is sufficient to create a travel time ratio less than one. Contrasts of this magnitude are often exceeded in alluvial environments and thus simultaneous measurement of solute and pressure has the potential to constrain estimates of exchange flux in a way not possible with pressure measurements alone. In general, flux estimates derived from solute travel times provide more accurate estimates than those derived from pressure responses in heterogeneous environments. The magnitude of error in estimates derived from pressure responses is proportional to the hydraulic conductivity contrast. Travel times calculated from time series pressure and EC data collected in the Mitchell River in northern Australia are used to demonstrate application of this combined approach.