In this paper, we study a multi-vehicle coverage control problem in constant flow environments while taking into account both energy consumption and traveling time. More specifically, the metric (called the mixed energy-time metric) is a weighted sum of the energy consumption and the traveling time for a vehicle to travel from one point to another in constant flows when using the minimum energy control, and the objective is to find vehicle locations that can minimize the expected mixed energy-time required for the set of vehicles to cover a region. We propose a gradient based control law which is calculated based on refined approximated Voronoi cells (induced by the mixed energy-time metric) and of which the convergence is proved via Hybrid Systems Theory. Simulations show that the refined gradient based control can achieve similar performance as the exact gradient based control. (C) 2013 Elsevier Ltd. All rights reserved.