The timing chain drives WP, it has a gear on the end of it. Vehicle has two serp belts, one for a/c-alt, the other power steering.
The car drives that far because the battery takes it that far before running down and then it has to be recharged. You won't get nearly so far at night, the lights use additional power. If the missing belt drove the water pump then 5 minutes and the engine would be scrap for the scrapyards.
A Youtube vid shows using a much shorter belt as possible but I found none listed in parts, probably because none of them came with no a/c. Look at the vid around 2:59, it shows nothing really in the way of a no a/c belt but the OP will have to carefully pick one that can work there, it will be MUCH shorter.
https://www.youtube.com/watch?v=ld-PK319w9c