# Midget 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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