Why the Long Face?

Consider the following figure:

Ciri and her horse Kelpie are standing at point AAA. She needs to go to a coffee bar located at point BBB. In front of them are the sand region (the shaded region) with width ADADAD and the grass region with width CDCDCD. Assume that both the grass region and the sand region extend towards infinity with the same respective width in both directions. Kelpie can go twice as fast over the grass than the sand. Ciri wants to ride her horse to reach BBB as fast as possible.

This is a companion discussion topic for the original entry at https://toph.co/p/why-the-long-face