Open-system processes have a large capacity to modify magma compositions during differentiation. Obtaining the rates of such processes is essential to understanding and constraining the evolution of magmatic systems. Here we quantify the time scales for magmatic assimilation of hydrous mafic to ultramafic cumulates by ascending basalts using the zoning patterns of olivine xenocrysts. Robust diffusion modeling results have been obtained by treating multiple compositional profiles for multiple elements (Fe-Mg, Ni, Mn, Ca) on multiple crystals from multiple flows. We find that the time between assimilation and eruption ranges from a few months to ∼25 yr, although 80% of the results are <10 yr. These ranges are shorter than either magma transport times from the mantle to the surface or typical repose periods of arc volcanoes. Thus, modification of the geochemical and mineralogical features of basalts by assimilation of plutonic rocks is a fast and probably unavoidable magmatic process.