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Topic: Highschool Math assignment question
Replies: 4   Last Post: Sep 18, 2007 12:02 AM

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Posts: 251
Registered: 12/6/04
Re: Highschool Math assignment question
Posted: Sep 18, 2007 12:02 AM
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"Pubkeybreaker" <> wrote in message
> Wes wrote:

>> I have this tricky question and i need some help
>> A tivetan monk leaves the monastery at 7 am and takes his usual path to
>> the top of the mountain, arriving at 7 pm. The following morning, he
>> starts at 7am at the top and takes the same path backm arriving at the
>> monastery at 7pm. using a grpah maybe, can you show that there must be a
>> point on the path that the monk will cross exactly the same time of day
>> on both days?
>> im not sure of what kind of graph i should be using
>> help will be much appreciated

> You don't use a graph. A graph would give a plausibility argument,
> but it would
> not be rigorous. Instead, you use the intermediate value theorem.

Since this is a high school problem that says "using a graph maybe" then no,
the answer is not to use a graph and be completely rigorous. The class
could very well not even know what IVT is. They are simply looking for a
graph of the relationship, and for the student to discover some interesting
things just by looking. probably posted in the wrong newsgroup, but since
its her lets answer the question, not a different question :-)

Simply sketch a graph, with the x-axis being time (7am, 7pm, 7am, 7pm) and
the y-axis being height of the mountain. Choose an arbitrary y since it
does not give a specific height. So you will go in a (sloped) straight line
up from 7am to the designated y point above 7pm, then straight across
horizontally to represent the time spent on the mountain, stopping at the
point above the next 7am, then sloped down again in a straight line to the
last 7pm on the x-axis.

/ \
/ \
/ \
7 7 7 7
a p a p

Something like that. Remember, the horizontal represents time and the
vertical represents height. Take a very close look at your sketch. If made
correctly, the two sloped lines will have opposite slopes, i.e. if you split
it in the middle it would by symmetric about the vertical line x=1am. This
represents the possibility the monk both climbed and descended the mountain
at the same (average) rate, which is what I see as the intended
interpretation of the problem, as unrealistic as it sounds.

What can be said about such a graph, and how does that translate as an
answer to the problem? Hint: You can make a _much_ bolder statement than
the one you are asked to make. If you cut out a figure with such a shape
and folded it over in the middle, would not the two slanted edges coincide?


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