Real Analysis question: By using Intermediate Value Theorem 'If f is a continuous real-valued function on an interval I, then f has the intermediate...
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Real Analysis question:

By using Intermediate Value Theorem "If f is a continuous real-valued function on an interval I, then f has the intermediate value property on I: Whenever a, b ∈ I, a < b and y lies between f(a) and f(b) [i.e., f(a) < y < f(b) or f(b) < y < f(a)], there exists at least one x in (a, b) such that f(x) = y."

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A wise person ascends a mountain continuously, starting up at 06:00 hrs. and arriving at the top at 18:00 hrs., then meditates through the night at the top and descends continuously the next day, starting down at 06:00 and arriving at the base at 18:00hrs. Prove that at a certain time of the day the wise person is at the same height on the way down as on the way up (the day before).

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Subject: Math
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