Say, one travels from Times Square (1451 Broadway New York, NY, 10036) to White House (1600 Pennsylvania Ave NW, Washington, DC 20500). For this 4+ hour drive, I would like to calculate the average road distance that needs to be driven in each COUNTY along the way. 

Note: 

* A road can cross the same state or same county couple or more times
* We can consider the default recommended road provided by Google maps API

I would like to have a recommendation on the approach to calculate the average distance in each county.