Three Valves, One Cistern

A caretaker needs to fill an empty cistern. The first inlet, working alone at a steady rate, can fill the entire cistern in three hours. A second inlet also runs steadily and would fill the cistern by itself in four hours. At the bottom is a drain that remains open; if the cistern started full and no water entered, this drain would empty it in six hours. The caretaker opens both inlet pipes and the drain at the same moment. Assume the flow rates stay constant, the cistern begins completely empty, and no water spills over. How long will it take for the cistern to become full?