Each Time Zone you cross changes the local time either ahead one hour or back one hour depending on if your moving east or west. The elapsed time just keeps accumulating.
I'm going to base these examples on a Saddle Sore 1000. A 1000 mile ride in less than 24 hours. That is of elapsed time from start to finish.
Example 1: SS ridden all on the same day. You started your ride somewhere and your DBR shows 06:00 AM. You drive 1010 miles or so to make sure you meet the distance and your ending DBR shows 10:00 PM. 16 hours has elapsed from start to finish. 6 before noon and 10 after.
Example 2: SS ridden across two days. You started your ride somewhere and your DBR shows 06:00 PM. You again drive the 1000+ miles or so and your ending DBR shows 10:00 AM the next day. 6 hours on the first day and 10 hours the next day. Again, 16 hours elapse from start to finish.
Example 3: SS ridden across time zones going west. You started your ride somewhere in the Eastern Timezone and your DBR shows 06:00 AM. As you drive the 1000+ miles you just happen to arrive at, and cross into, the Central Timezone at noon (It makes the math easy that way). You continue your ride and your ending DBR shows 9:00 PM. Using the math from the examples above, it appears that you were able to shave a whole hour off your ride and completed the required distance in 15 hours. 6 hours in the Eastern Timezone and only 9 in the Central Timezone. Good Job! However this is not the case. As you move west, local time decreases by one hour each time you cross into a different timezone. Therefore you must add an hour to the local time at the finish to get the correct elapsed time which in this case is still 16 hours. The opposite is true going east. You must subtract an hour from the local time when you cross into a different timezone to fine the correct elapsed time. The elapsed time is what is important. A stop watch displays elapsed time.
The graphic below shows the timezone of the United States. Think of the sun rising in the east and setting in the west and where the sun is in the sky at your location at noon (Directly overhead) and where it is in other parts of the country. Then think of where the sun will at your location when it is noon in the other locations. I hope this helps and I haven't confused you more.