A monk set out from a monastery in the valley at dawn. He walked all day up a wi
ID: 2881028 • Letter: A
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
Explanation / Answer
Yes, there is a point along the path that monk occupied at the same time of day on both journeys.
Simply, forget that the journey occured at two different times. Instead imagine the monk and his twin making the ascent and descent simultaneouly. There can be no doubt that the two monks must pass each other at the same point along the trail - at the same time of day.