A water tank is fitted with four different taps as outlets. If the tank is full, it takes $$1\ \text{hour}$$ to empty the tank when the first tap alone is opened, it takes $$2\ \text{hours}$$ to empty the tank when the second tap alone is opened, it takes $$3\ \text{hours}$$ when the third tap alone is opened and $$4\ \text{hours}$$ to empty the tank when the fourth tap alone is opened. . When all the taps are opened simultaneously, the full tank will be emptied in