mathematics - A crawling spider and a cautious fly

Inside a rectangular room, measuring 16 feet in length and 8 feet in width and height, a spider resides at a corner. A fly buzzing in the room intends to land at a spot that will take the spider the longest to reach, knowing that the spider never drops or uses its web, but crawls at constant speed.

Where should the fly land?

Answer

The optimal distance seems to be

$\sqrt{14^2+18^2} = \sqrt{22^2+6^2} \approx 22.804$
which is greater than
$\sqrt{16^2+16^2} \approx 22.627$
If the fly stayed at the opposite corner.

Assuming the spider is on the roof corner, be in the opposite corner (on the floor), then move upwards 2 feet and sideways 2 feet.

The key to this puzzle is that there are 4 distances to be optimized.