Problem 3

## Up And Down The Mountain

One day at noon, Annie runs to the top of a mountain. She sits and ponders the meaning of life until the next day at noon at which time she runs down the mountain along the same trail that she ran up. Was she necessarily at some point on the mountain trail at the same time on both days? Prove your answer — Mr. Simmons

Alright cool. This doesnt seem too tricky. How bout we give each point on the mountain a number. Lets say the mountain is 100 yards.
so it could look kinda like this:

000 10 20 30 40 50 60 70 80 90 100

Bot……………………………………………………Top

but on the way don it would look like:

100 90 80 70 60 50 40 30 20 10 000
Top…………………………………………………..Bot.
so it looks like only at the half way point she would be at the same place, assuming she went the same speed.

Travis P.

I agree with you too, Travis. I think it is the same place too. Here is my diagram.

0 10 20 30 40 50 60 70 80 90 100

This is how the mountain looked like when she was climbing it.

0 10 20 30 40 50 60 70 80 90 100
------ ------
50 yards is where she is.

100 90 80 70 60 50 40 30 20 10 0

On her way down, the moutain looked like this.

100 90 80 70 60 50 40 30 20 10 0
------ -----—-
At noon, she is at 50 yards.

The moutains looks different and everything from the top or bottom view, but the middle or 50 yards will always be the same. (Look from the edited because looks really bad)
- Christine N. :)

I don't think she would be at the same point at any time because it doesnt say how fast she was running and she could have tripped on the way down so i dont think there's an exact point where she was at on both days.
Tyler W.

I think you are right! What if you walks slower or faster? We cannot really control how fast so walks. So I guess the answer is no. No, she will not be at the same place.
- Christine N. :)

page revision: 95, last edited: 28 May 2009 01:29