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If This Is Fair?

Word origins fascinate me. For example, any idea where the word "hitch-hiker" came from?

Supposedly, two men went on a journey together, but had only one horse between them. One man rode the horse a specified distance, dismounted, hitched the horse to a tree, and then continued walking down the road. The other man started out walking, until he got to the horse, which he mounted and rode until he caught up with his fellow hiker....and the process was repeated.

Other than being interesting...there must be some mathematics here. My question: Under what conditions will this hitch-hiking process be fair?

Source: Oscar Ameringer's If You Don't Weaken, 1983