Running Paths

Geometry Level 1

Alice and Bob are standing at the point marked Start on the perimeter of a park (the large, outer square). The park also has a smaller, inner square formed by joining the midpoints of its sides.

Bob starts running around the inner square and, at the same time, Alice starts running around the outer square. Both run at the same speed.

If they keep running, will they ever be in the exact same location again at the same time?

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