A mechanical engineer, in charge of developing the plumbing system for a new hotel in Vail, has been informed that the city$-$supplied water main tap for the hotel will be $80$ psi. The engineer has to determine the maximum number of floors that can be reached using a typical upfeed distribution system. Each floor of the hotel will be $12$ft in height. The hotel owner would like as many floors as possible to increase the total occupancy of the hotel. Each hotel room will utilize a bathroom group with gravity tank water closets that will require $20$ psi each. Therefore, the room furthest away from the water main on the top floor will require $20$ psi. Ignoring friction loss and other fixtures, find the total vertical distance that can be achieved based on the conditions listed above. Then, using the total vertical distance, find the total number of floors that this hotel can be designed for.