The Palace of Jzork

On an expedition, Betsy comes across the lost of world of Jzork. To visit the Empress, Betsy must make her way around a triangular-shaped palace.

Betsy is at Point D while the Empress is at Point G. The palace (ABC) is equilateral, as are all the rooms inside the palace (the interior triangles). The distance from Point A to Point B is 100 meters.

The palace has moving sidewalks, shown in green, which can take Betsy to the Empress. Around the perimeter of the palace the speed of the sidewalk is 5 meters/second. While the sidewalks inside the palace have a speed of 2 meters/second.

What is the quickest path Betsy can take to see the Empress? What distance will Betsy cover to reach her, and how long will it take her?

See the solutions