Question

A monk set out from a monastery in the valley at dawn. He walked all day up a winding​ path, stopping for lunch and taking a nap along the way. At​ dusk, he arrived at a temple on the mountaintop. The next​ day, the monk made the return walk to the​ valley, leaving the temple at​ dawn, walking the same path for the entire​ day, and arriving at the monastery in the evening. Must there be one point along the path that the monk occupied at the same time of day on both the ascent and​ descent? (Hint: The question can be answered without the Intermediate Value​ Theorem.)

choose correct answer :
No
Yes

Answer 1

Yes, there must be at least one point along the path that the monk occupied at the same time of day on both the ascent and descent, as demonstrated by imagining two monks starting from opposite ends at the same time and meeting at some point.

Step-by-step explanation:

The question posed is a classic problem related to the concept of continuous functions and can be elegantly addressed with a thought experiment. Must there be one point along the path that the monk occupied at the same time of day on both the ascent and descent? The answer is Yes.

Imagine two monks beginning at dawn, one starting from the monastery and the other from the temple. They walk the same path but in opposite directions and, since they start and end their journeys at the same times, they must meet at some point along the path. That meeting point is where they are at the same spot at the same time of day on both days. This logic doesn't require the Intermediate Value Theorem; it relies on the simple premise that to travel from one point to another and back, a path must be crossed.