CALLING ALL MATH GEEKS: Math Puzzle

from JoeUser Forums
OK, so my Calc teacher gives the class this math problem, and I cannot figure it out. I have tried and tried, but each idea that I get can be reasoned away to nothing. Post your hints, ideas, or solutions(I'd rather you not, but feel free, I wont delete your post.)

Two towns, A and B, are located along the Appalachian Trail. At sunrise, Pat begins walking south from A to B along the trail, while simultaneously Dana begins walking north from B to A. Each person walks at a constant speed, and they cross paths at noon. Pat arrives in B at 5pm while Dana reaches A at 11:15 pm.

When was sunrise?
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5,681 views 5 replies
Reply #1 from JoeUser Forums Top
When the sun rose.  Insuffient information to calculate a numerical solution, so the solution must be logical.
Reply #2 from JoeUser Forums Top
When the sun rose. Insuffient information to calculate a numerical solution, so the solution must be logical.

I knew you'd have the answer!! ROFL
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Reply #3 from JoeUser Forums Top
That is what I was pondering. My thoughts were: A) It was cloudy in one area, and not in the other. B) One person teleports C) Solar Eclipse

Any other ideas? Besides the fact that it must be logical lol?
Reply #4 from JoeUser Forums Top
Okay, after two scratch pads, numerous equations punched into a spreadsheet, and little over an hour, I solved it. (I'm slowing down in my old age.)


(NOTE: Each of the following paragraphs gives you progressively more information on how to solve the problem. If you really want to solve it yourself, you might like to stop at the information provided by each paragraph, go attempt a solution, then only come back to the next when you're stuck.)


The biggest mistake you're making is that while it says they walked at a constant rate, it does not say they walked at the same constant rate. Obviously one is walking faster than the other.

Focus on the numerous constants:
Arrival times
Crossing time
Sunrise (it's a constant even though you aren't given it)
Distance (another constant)

The crossing point is a percentage of the whole distance/time. For instance, if it was 50%, given just the 5 P.M. arrival you would know half the trip took 5 hours, the whole trip took 10 hours, and sunrise was at 7 A.M. But since they are traveling at different (though constant) paces, the crossing point isn't at 50% of the distance.

The two walkers just give you a way to prove your answer. When you find the percentage for one, the inverse applies to the other. That gives you an elapsed time for each. That gives you the starting time (i.e. sunrise) for each.

It's basically a matter of what percentage of the entire distance did the crossing point came at, using the two walkers' elapsed times to prove it, and playing with that percentage till the starting times equal.
Reply #5 from JoeUser Forums Top
, in my young age I talked to another friend of mine, and we spent over two hours on AIM trying to figure it out. I think I got a ratio or somethign like that, I dunno it was really late. However I was thinking that it was somethign like the total number of hours it took for the slow walker divided by the total number of hours it took for the faster walker, to see the rate at which they moved. I made an assumption that the average deviation from sunrise would be about 1.5 hours, and just started finding the rate at this time, and this time, and this time, etc. But I could not conclude the exact rate, or the reason why I got the rates I did, or even what the rate was that I finally got (2 a.m. and very hungry at the time). I had a heck of a lot of fun reasoning this out, making some really crazy ideas, like cloudiness and such that really had no bearing on the solution, but it was fun debating with some of my friends, and posting here, trying to find the answer. I failed, but I am still very curious to see your data. Would you oblige to post your solution, and the system that you found it with?