# 5-year olds shouldn't circumnavigate alien planets

Geometry Level 2

Susan is 5 Earth years old. She is also exactly 1 meter tall. On the planet Floobenweifer, there lives a race of aliens called Floobs that kills humans at night. To avoid the night, Susan walks faster than the planet is rotating, to keep ahead of sunset. The planet has a diameter of 500 kilometers, and she walks at 200 km/h. After completing a whole walk around the entire circumference of the globe, let $$X$$ be the difference between the distance Susan's feet go, and the distance the top of Susan's head goes. If $$X$$ can be expressed as $$a\pi$$, find $$a$$.

Details and assumptions

• Susan's feet never leave the ground.

• Floobenweifer is a perfect sphere.

• No Floobs or little girls were harmed during the making of this problem.

• Susan is an insane runner.

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