Pre-Calculus

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Can I solve this with trig? It reminds me of a trig question, yet I don't know what to do, thanks.

A Tibetan monk leaves the monastery at 7:00 am., and takes his usual path to the top of the mountain, arriving at 7:00 pm. The following morning, he starts out at 7:00 a.m. at the top and takes the same path back, arriving at the monastery at 7:00 pm. Using a graph maybe, can you show that there must be a point on the path that the monk will cross at exactly the same time of day on both days?

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Try using an x,y-graph. Let "x" be the time and "y" be his height. (Pick some random number for the altitude at the peak, or just label it as "h" or something.) Don't bother trying to be real specific. The point is that, on day 1, he starts at (0, 0) and ends up at (7, h), and he never goes below y = 0 and never goes above y = h. Also, since he can't instantaneously travel from one spot to another, higher, spot, he must trudge through every altitude from 0 to h. So draw some line, straight or wiggly, from (0, 0) to (7, h), staying strictly between y = 0 and y = h.

On day 2, he starts at (0, h) and goes to (7, 0). Draw a line.

Is there any way, within the limitations of this exercise, to draw these lines so that they don't cross each other?

Eliz.
 
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