The response of hillslope processes to changes in precipitation may drive the observed changes in the solute geochemistry of rivers with discharge. This conjecture is most robust when variations in the key environmental factors that affect hillslope processes (e.g., lithology, erosion rate, and climate) are minimal across a river's catchment area. For rivers with heterogenous catchments, temporal variations in the relative contributions of different tributary subcatchments may modulate variations in solute geochemistry with runoff. In the absence of a dense network of hydrologic gauging stations, alternative approaches are required to distinguish between the different drivers of temporal variability in river solute concentrations. In this contribution, we apportion the water and solute fluxes of a reach of the Madre de Dios River (Peru) between its four major tributary subcatchments during two sampling campaigns (wet and dry seasons) using spatial variations in conservative tracers. Guided by the results of a mixing model, we identify temporal variations in solute concentrations of the main stem Madre de Dios that are due to changes in the relative contributions of each tributary. Our results suggest that variations in tributary mixing are, in part, responsible for the observed concentration‐discharge (C‐Q) relationships. The implications of these results are further explored by reanalyzing previously published C‐Q data from this region, developing a theoretical model of tributary mixing, and, in a companion paper, comparing the C‐Q behavior of a suite of major and trace elements in the Madre de Dios River system.