I am trying to figure out how best to calculate a 1.5 and 2.5-mile driving distance from a single point. Let's say we have a Fire Station connected to a road network and you want to find the 1.5 and 2.5-mile maximum driving distance along the road, is this possible?
It is definitely possible, but you'll need a license for Network Analyst or Spatial Analyst. Here's a good resource for just what you're trying to do with Network Analyst: http://desktop.arcgis.com/en/arcmap/latest/extensions/network-analyst/types-of-network-analyses.htm. If you have only Spatial Analyst, you could use Cost Distance. In that situation you'd need to create a raster layer with all roads having some raster value, and all areas impassable to vehicles as NoData. You could even assign different weights to different road classes (i.e. freeways = 1, city streets = 4, access roads = 5, gravel roads = 8, etc.) with Reclassify. Then select your source point and calculate Cost Distance (make sure to set Processing Extents to the original raster limits in Environments), which will produce a new raster. Finally, Contour will give you the distance contours you're looking for.