Or at least get me started...

One morning at 7am a man begins his way up a mountain along a path. He ascends at a varying rate of speed. He stops at a spot for lunch. He reaches the top at sunset where he spends the night. The next morning at 7am he starts down again along the same path. Again, he desends at an undetermined speed and stops at a spot for lunch.

Edit: Prove that the the man stops at the exact same spot for lunch at precisely the same time on both days.

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You don't need a weatherman to know which way the wind blows - Robert A. Zimmerman

He had tuna on rye. And a beer.

But seriously, I'm not sure... What is the question?

MV

I should read my post before posting.

Prove that the man stops at the exact same spot for lunch at precisely the same time on both days.

__________________
You don't need a weatherman to know which way the wind blows - Robert A. Zimmerman

I'm not sure that can be proved mathematically, at least not with the info given. Did you try asking the guy? Or maybe seeing if he took pictures during his lunch?

MV

there is only one macdonalds on the way up.

Tom W

__________________
[SIGPIC] Diesel loving autocrossing grandpa Architect. 08 Dodge 3/4 ton with Cummins & six speed; I have had about 35 benzes. I have a 39 Studebaker Coupe Express pickup in which I have had installed a 617 turbo and a five speed manual.[SIGPIC]

..I also have a 427 Cobra replica with an aluminum chassis.

Is the undetermined speed on the way down constant? Compared to the variable speed on the way up? Are we supposed to write an equation showing this?

Given, it's been a while since any of my math classes, but this seems to me to be something I can write an equation showing, but not something I can prove, in the mathematical sense.

MV

Apparently speed doesn't matter. It's just noise.

I don't suppose you need an equation. You can show it any way you want. You need to show that there exists one spot along the path, anywhere on the path, where the man stops for lunch at exactly the same time each day.

__________________
You don't need a weatherman to know which way the wind blows - Robert A. Zimmerman

Ok if it is not the macdonalds, then there is only one place to sit down and eat, right?

Tom W

__________________
[SIGPIC] Diesel loving autocrossing grandpa Architect. 08 Dodge 3/4 ton with Cummins & six speed; I have had about 35 benzes. I have a 39 Studebaker Coupe Express pickup in which I have had installed a 617 turbo and a five speed manual.[SIGPIC]

..I also have a 427 Cobra replica with an aluminum chassis.

So all we have to do is show that there is one spot equal distance between two points? Nothing else?

This is why I lost interest in most math and science long ago. You need an equation to show that there is a middle to a journey? Seriously, math teachers need to get out more often.

My best moment in math was getting test credit for sex. My best moment in science was negotiating to keep the grade I had changed in the computer in exchange for letting the teacher know her new password and access the rest of the years work, followed closely by the time I had an exhaustive debate with a physics teacher about monkey hunting (the correct answer is to aim at the monkey).

The real world varies so much from the classroom that at times it's almost useless to try and combine the two.

MV

If an equation isn't needed try this:

..........T
........./
......../
....../
.....M
..../
.../
../
B

where: B=bottom
M=middle (lunch)
T=top

Consider it a "Graphical Representation"

MV

Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing... It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true... If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. -Bertrand Russell

__________________
-Marty

1986 300E 220,000 miles+ transmission impossible
(Now waiting under a bridge in order to become one)

Reading your M103 duty cycle:
http://www.peachparts.com/shopforum/showpost.php?p=831799&postcount=13
http://www.peachparts.com/shopforum/showpost.php?p=831807&postcount=14

No you need to show that there exists definitely one point but it can be anywhere on the line that would hold for any speed of ascent or descent as long as the total time of ascent is equal to the total time of descent.

__________________
You don't need a weatherman to know which way the wind blows - Robert A. Zimmerman

OK wait just replace speed with time. Thanks BAV even though you didn't "solve" it you did give me an idea.

That's an accepted method of proof, graph theory.

__________________
You don't need a weatherman to know which way the wind blows - Robert A. Zimmerman

Would the fact that the time of lunch is the same help to locate the lunch point?

__________________
-Marty

1986 300E 220,000 miles+ transmission impossible
(Now waiting under a bridge in order to become one)

Reading your M103 duty cycle:
http://www.peachparts.com/shopforum/showpost.php?p=831799&postcount=13
http://www.peachparts.com/shopforum/showpost.php?p=831807&postcount=14

Slow down! You're thinking faster than I can write.

__________________
-Marty

1986 300E 220,000 miles+ transmission impossible
(Now waiting under a bridge in order to become one)

Reading your M103 duty cycle:
http://www.peachparts.com/shopforum/showpost.php?p=831799&postcount=13
http://www.peachparts.com/shopforum/showpost.php?p=831807&postcount=14