Wireless sensor networks provide long-term monitoring of the environment, but sensors are powered by small batteries. Using a mobile charger (MC) to replenish energy of sensors is one promising solution to prolong their usage time. Many approaches have been developed to find the MC's moving path, and they assume that sensors have a fixed sensing rate (SR) and prefer to fully charge sensors. In practice, sensors can adaptively adjust their SRs to meet application demands or save energy. Besides, due to the fully charging policy, some sensors with low energy may take long to wait for the MC's service. Thus, the paper formulates a path and charge (P&C) problem, which asks how to dispatch the MC to visit sensors with adaptive SRs and decide their charging time, such that both survivability and throughput of sensors can be maximized. Then, we propose an efficient P&C scheduling (EPCS) algorithm, which builds the shortest path to visit each sensor. To make the MC fast move to charge the sensors near death, some sensors with enough energy are excluded from the path. Moreover, EPCS adopts a floating charging mechanism based on the ratio of workable sensors and their energy depletion. Simulation results verify that EPCS can significantly improve the survivability and throughput of sensors.