Final answer:
The gas station should be built at the circumcenter of the triangle formed by the three main roads, which is the point where the perpendicular bisectors of the triangle's sides meet and is equidistant from each road.
Step-by-step explanation:
The mayor wants the new gas station to be the same distance from the three main roads in town. This implies that the gas station should be built at the point of concurrency known as the circumcenter of the triangle formed by the three main roads. The circumcenter is the point where the perpendicular bisectors of the sides of the triangle meet, and it is equidistant from the vertices (the points of intersection) of the three main roads. To find this point, one would draw the three main roads as line segments, construct perpendicular bisectors for each, and determine where they intersect.
Given the various conditions described in the scenarios, such as traffic increases, business expansions, and geographical considerations like distances and travel times, determining the location for the gas station involves not only geometric constructions but also practical considerations regarding traffic flow and accessibility.