The ongoing electrification of powertrains requires innovative solutions that allow a broad application of battery electric vehicles (BEVs) with respect to different driving tasks. Especially long distance journeys for fully electric vehicles are a major obstacle due to range anxiety, the need to recharge and the lack of precise information on the driving and charging scenarios needed. An optimal strategy that consists of velocity as well as charging suggestions enables a seamless use of electric vehicles on long distance journeys. Through a dynamic programming (DP) approach, a global time optimality of driving and charging tasks for two use cases is derived and presented. The existing control levers of vehicle speed and charger choice as well as the amount of charged energy are varied in their discretization. This is done under the aspects of overall travel time and a final state constraint. With regard to its computing time, the parameters' discretization is discussed. The applicability of the problem specific method is shown, optimal strategies are calculated. Also, it can be shown that the course of the state variable, i.e. the vehicles state of charge (SOC) dominates sensitivities in time and state deviation.