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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