Signaling events in eukaryotic cells are often guided by a scaffolding protein. Scaffold proteins assemble multiple proteins into a spatially localized signaling complex and exert numerous physical effects on signaling pathways. To study these effects, we consider a minimal, three-state kinetic model of scaffold-mediated kinase activation. We first introduce and apply a path summation technique to obtain approximate solutions to a single molecule master equation that governs protein kinase activation. We then consider exact numerical solutions. We comment on when this approximation is appropriate and then use this analysis to illustrate the competition of processes occurring at many time scales that are involved in signal transduction in the presence of a scaffold protein. We find that our minimal model captures how scaffold concentration can influence the times over which signaling is distributed in kinase cascades. For a range of scaffold concentrations, scaffolds allow for signaling to be distributed over multiple decades. The findings are consistent with recent experiments and simulation data. These results provide a framework and offer a mechanism for understanding how scaffold proteins can influence the shape of the waiting time distribution of kinase activation and effectively broaden the times over which protein kinases are activated in the course of cell signaling.