21 Tetrahedron

© Frauke Jansen, MATH+

Author:  Henni ter Morsche (TU Eindhoven)
Project: 4TU.AMI

Challenge

A black and a green bug are sitting on a regular tetrahedron ABCD. The black bug starts its journey at 4 pm at vertex A, crawls with constant velocity along the edge AB, and reaches vertex B at 6 pm. The green bug starts its journey at 4 pm in vertex C crawls with constant velocity along the edge CD, reaches vertex D at 5 pm, and then stays sitting in D.

We want to know from you: at which point T in time are the two bugs at minimum distance* from each other?

*Note: We are looking for the minimum distance in threedimensional space, not on the surface of the tetrahedron.

Possible answers:

1. At time T = 4:31 pm.
2. At time T = 4:32 pm.
3. At time T = 4:33 pm.
4. At time T = 4:34 pm.
5. At time T = 4:35 pm.
6. At time T = 4:36 pm.
7. At time T = 4:37 pm.
8. At time T = 4:38 pm.
9. At time T = 4:39 pm.
10. At time T = 4:40 pm.