The coupled-tank system, a classic example of a non-linear dynamical system, serves as a benchmark for evaluating advanced control and estimation techniques. The primary objective in controlling such a system is to regulate or maintain liquid levels in the tanks at desired set points, providing valuable insights into the dynamics of fluid flow within interconnected networks. In this study, we present a novel contribution by developing and simulating a time-optimal control strategy for a two-tank coupled system using MatLab. The proposed approach employs a single open-loop control law, leveraging the bang-bang structure inherent to time-optimal control, as derived from the necessary conditions of the Pontryagin Maximum Principle (PMP). To achieve high precision, we utilize an approximate solution obtained through a direct discretization method as an initial guess for the shooting method, which is rooted in the indirect approach of the PMP. This hybrid methodology not only enhances computational efficiency but also yields a more accurate and reliable solution, demonstrating the effectiveness of combining direct and indirect optimal control techniques for complex non-linear systems.