Choosing an Elevator

Two elevators leave the nth floor at 2:00 P.M. The faster elevator takes one minute to travel between floors and the slower elevator takes two minutes to travel between floors. The first elevator to reach a floor must stop for three minutes to take on passengers. If both elevators arrive at a floor at the exact same time, they become confused and do not stop for passengers.

If the final stop for an elevator is the lobby (1st floor), then describe n if the faster elevator arrives at the lobby first. Describe n if the slower elevator arrives at the lobby first.
(Source: Mathematics Teaching in the Middle School, Apr 1994)