Motor learning occurs through multiple mechanisms, including unsupervised, supervised (error-based) and reinforcement (reward-based) learning. Although studies have shown that reward leads to an overall better motor adaptation, the specific processes by which reward influences adaptation are still unclear. Here, we examine how the presence of reward affects dual-adaptation to novel dynamics, and distinguish its influence on implicit and explicit learning. Participants adapted to two opposing force fields in an adaptation/de-adaptation/error-clamp paradigm, where five levels of reward (a score and a digital face) were provided as participants reduced their lateral error. Both reward and control (no reward provided) groups simultaneously adapted to both opposing force fields, exhibiting a similar final level of adaptation, which was primarily implicit. Triple-rate models fit to the adaptation process found higher learning rates in the fast and slow processes, and a slightly increased fast retention rate for the reward group. While differences in the slow learning rate were only driven by implicit learning, the large difference in the fast learning rate was mainly explicit. Overall, we confirm previous work showing that reward increases learning rates, extending this to dual-adaptation experiments, and demonstrating that reward influences both implicit and explicit adaptation. Specifically, we show that reward acts primarily explicitly on the fast learning rate and implicitly on the slow learning rates.