Mathematics · Time and Work

A water tank can be filled by two identical inlet pipes, each capable of filling the tank in 12 hours. There is also an outlet pipe that can empty the full tank in 15 hours. The two inlet pipes are kept open continuously, while the outlet pipe is opened for 1 hour after every 2 hours of its closure (i.e., inlets run for 2 hours, then all three run for 1 hour, and so on). Find the total time required to completely fill the empty tank.