At some point each day they will be on this path at the same point in time in the same location.

Go back to the previous thread and look at the graph that Biff posted. At first he was confused by it but after a bit of thinking he understood it and his graph depicts the situation adequately.

You are dealing with an indefinite number of time points. As long as there is no possible way that the person in question can have there places on the paths cross during that one or two minute difference between sunrise times are sunset times each day, and as long as the person is on the exact same path each way, the situation must play at 100% of the time.