Help solving and reasoning a word problem.

I need to know how to solve this problem. This is the information I was able to write down. Hopefully, someone has heard of it before and can tell me how to solve it.

A priest takes a pilgrimage to a hill every morning. He steps on the path at 6:00 am and stays on the path until he reaches the top of the hill. Six hours later, he arrives and reaches the top of the hill at 12:00 noon.

Then, he turns back and starts again, but at some point in the journey, he will reach a specific point at exactly the same time and same place both trips. What goes on from 6:00 am to noon time is up to the individual.

How can this take place?