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

Your Thoughts…

yay! im first! well anyways i read it and i think it would be at the midway point. Ut wouldnt it depend on her speed?

~~ Maha A.

Wait.. i just thought about it and it wouldnt matter because if she went really slow going up and really fast going down, then the piont would just be higher up i think and vice versa.

~~Maha A.

Well, she would probably go faster on the way down.. so she would never be at the same point at the same time.
-Courtney W.

For now, I agree with Courtney. On the way down, since she is running down on a slope, she would obviously go faster. (but isn't the solution too simple then?)
-Jane L.

She doesnt neccesarily have to go faster down, like what if she run up and walks down, then gravity couldnt make up that big a differencee so i think it depends on speed. if it is a constant speed up and down then it is middway but it doesnt specify about speed so i dont know..

~~Maha A.

But still it is really unlikely you go the EXACT same speed both times (unless you have some weird speed calculator) so it would be no. But Jane's right, that does seem to easy.. and doesn't neccessarily mean 'have to' so she doesn't Have to be at the same point at the same time.. (maybe im over thinking it?) i might be wrong

~~Maha A.

Didn't Mr. Simmons say in class one time that the answer is simple but you have to prove it, so maybe that is the answer we just have to prove it..

~~Maha A.

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