The Hiking tour!!!!

The Mountain Climbing

On Monday morning at 9:00 am you start at the base of a mountain and begin hiking. Your pace is not regular and you take breaks along the way. Monday evening at 9:00 pm you reach the peak. On Tuesday morning at 9:00 am, after camping overnight, you start at the peak of the mountain and begin your return trip. You follow the exact same path from the previous day, but your pace is faster and you take more breaks. Tuesday evening at 9:00 pm you reach the base. Can you determine if there is a point you were at somewhere on the path at the same time of day Monday and Tuesday. (You are not asked to name the point, just whether or not such a point must exist.)
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