Help with brain teaser?

Question

so....A monk climbs a mountain. He starts at 8 AM and reaches the summit at noon. He spends the night on the summit. The next morning, he leaves the summit at 8 AM and descends by the same route that he used the day before, reaching the bottom at noon. Prove that there is a time between 8 AM and noon at which the monk was at exactly the same spot on the mountain on both days. ( notice how theres no specifications about the speed that the monk travels.)

correct answer and explantion will be rewarded 11 points.

Answer 1

There is no way to prove when and where they pass, but you can prove that they must be at exactly the same point at the same time.

Here is the proof:

Imagine taking a video of the monk going up the hill, and then going down the hill.... Then overlay the videos over top of each other and play the single video back.  One monk will be going down and one will be coming up... and they WILL cross paths at some point in time.

You can speed up one monk, or slow the other monk down... but no matter how many different speeds you play them at when you put them together, they must always cross paths and be at exactly the same place at the same time.  

Another way to think about it is to have a "ghost climber" that exactly duplicates the monks climb up the mountain the same time the monk climbs down the mountain.  Again, it dosen't matter how fast the monk climbed up the mountain, or climbed down the mountain, the "ghost monk" and the monk MUST cross paths somewhere along the climb, therefore proving there were in the same place at the same time.

Answer 2

he was

Answer 3

it would be like half way to the bottom

or half way from the top :D  

Answer 4

If the monk traveled the same speed, at 10:30 am he would have been at the same spot.

Answer 5

get it on? wtf? hahaha