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Time is not taken into the amount of work done in an equation. Calories use work in the calculation of a calorie. Hense running a mile and walking a mile you have the same amount of weight moved the same distance, so same amount of work done.
Yes you burn the same amount of calories running and walking a mile. You are thinking how worked up your body is while running as opposed to walking, but make sure to take into account it's over a much briefer period than walking is. In the end they equal out to the same amount burned, just walking does it much slower.
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