"Pubkeybreaker" <email@example.com> wrote in message news:firstname.lastname@example.org... > > 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?