This paper extends the Arc Orienteering Problem (AOP) to large road networks with time-dependent travel times and time-dependent value gain, termed Twofold Time-Dependent AOP or 2TD-AOP for short. In its original definition, the NP-hard Orienteering Problem (OP) asks to find a path from a source to a destination maximizing the accumulated value while not exceeding a cost budget. Variations of the OP and AOP have many practical applications such as mobile crowdsourcing tasks (e.g., repairing and maintenance or dispatching field workers), diverse logistics problems (e.g., crowd control or controlling wildfires) as well as several tourist guidance problems (e.g., generating trip recommendations or navigating through theme parks). In the proposed 2TD-AOP, travel times and value functions are assumed to be time-dependent. The dynamic values model, for instance, varying rewards in crowdsourcing tasks or varying urgency levels in damage control tasks. We discuss this novel problem, prove the benefit of time-dependence empirically and present an efficient approximative solution, optimized for fast response systems. Our approach is the first time-dependent variant of the AOP to be evaluated on a large scale, fine-grained, real-world road network. We show that optimal solutions are infeasible and solutions to the static problem are often invalid. We propose an approximate dynamic programming solution which produces valid paths and is orders of magnitude faster than any optimal solution.