Predicting battery rate performance traditionally relies on computation-intensive numerical simulations. Although faster, simplified analytical models exist, they usually assume a single rate-limiting process such as solid diffusion or electrolyte transport. Here, an improved analytical model, the uniform-reaction-solid-concentration (URCs) model, is developed for battery (dis)charging under mixed control of mass transport in both solid and electrolyte phases. Compared to previous single-particle models extended to incorporate electrolyte kinetics, URCs captures the impact of salt depletion on diminishing the (dis)charge capacity, a critical phenomenon for thick electrodes and/or at high rates. The model demonstrates good agreement with full-order simulations. Importantly, it is compatible with gradient-based optimization algorithms to efficiently search for the optimal battery configurations, while the numerical simulation method struggles to accurately evaluate the derivatives of the objective function and causes optimization to fail. These features allow our model to effectively complement numerical simulations as a useful computational tool for battery design.