Intermediate Value Theorem

Can somebody help me set this one up, please? I can't quite see how the intermediate value theorem can be directly applied to this.

"A person walks up to the top of a mountain and camps for the night. On the next day, he returns to his car following the same path that he took the previous day. On each day, he starts and finishes his hike at the same time. Use the intermediate value theorem to show that there is a point on the path that the person will cross at exactly the same time of day on both days."

Thanks!