Logic puzzle
A sage stays atop a mountain in the Himalayas. Every morning he starts at 5:00 and reaches the foothills at 9:00. He travels non-uniformly, walking leisurely at times and at times breaking into a trot. He also takes rest at some points, but never digresses from his path. In the evening he starts at 5:00 to climb up in the same manner on the exact same path and reaches the top exactly at 9:00.
On any given day, will the sage be at any point on his route at the same time in the morning and evening?
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It's possible however very unlikely

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