If it is any help in explaining time zones, here is a example of part of a trip I have taken many times.
I leave Amarillo, Texas at 12:00 Noon, Central Standard Time
I reset the trip odometer on my car to 0.0 miles
The travel distance between Amarillo, Texas and the Glenrio, New Mexico Visitor Center at the Texas-New Mexico State Line is 72.7 Miles and the travel time is 1 Hour, 7 minutes
I arrive at the Travel Center at 1:07 PM Central Standard Time
As I am entering the Mountain Standard Time Zone going west, I set my watch back 1 hour to 12:07 PM Mountain Standard Time
The travel distance between the Visitor Center and Tucumcari, New Mexico is 40.4 miles and the travel time is 39 minutes
I arrive at Tucumcari at 12:46 PM Mountain Standard Time
I have traveled a total of 113.1 Miles and my total time travel time has been 1 hour and 46 minutes from Amarillo to Tucumcari.
Going east or west, the actual travel distance (113.1 Miles) and the actual travel time ( 1 hour and 46 minutes )} would always be the same.
But going east , I would set my watch ahead 1 hour at the state line.
If I left Tucumcari at 12:00 Noon Mountain Standard Time , I would arrive at the Visitor Center at 12:39 PM Mountain Standard Time and set my watch ahead 1 hour to 1:39 PM Central Standard Time entering Texas and arrive at Amarillo at 2:46 PM Central Standard Time.
I hope this might explain how time zones work on an actual trip.
If it didn't just muddy up the waters, my apologies. :-)
Source for distances and times from "distances between us cities " website
I might add that somewhere, and at some location and at some time, solar time and standard time in that time zone agree....Thanks, JackBlack ! :-)