Energy-harvesting technologies are currently under development to provide power for wireless networks and devices. This paper investigates the usage of radio frequency ( RF) signals emitted from wireless nodes as sources in energy-harvesting systems. The system we consider consists of multiple RF source nodes, multiple destination nodes, and an energy-harvesting node with a limited-capacity rechargeable battery. We observe that the total received power at the antenna of the harvesting node changes with the number of RF source nodes and the channel conditions. At the same time, the variation of instantaneous received power and the selected modulation type affect the required time for recharging battery. We study statistical models for the battery recharging time in the presence of multiple RF source nodes and focus on the generalized-K channels that include both large-scale and small-scale fading models. Then, we propose a distribution for the battery recharging time that provides a close and analytically tractable expression. We derive the associated fundamental statistical expressions for the battery recharging time in closed form. The simulations and numerical studies are used to verify the theoretical results. The Gamma distribution provides tight approximation to simulation results in fading wireless channel conditions. Additionally, we present battery recharging test results for two sources as a real-life application of energy harvesting with multiple RF sources. Our test results show close fit with the derived distribution equations, supporting theoretical analyses.