PUZZLE #4: BUG IN A SHOEBOX

I saw a puzzle very much like this when I was in high school, and (sigh) I got it wrong. See if you can get it right.

An empty lidless shoebox measures 3 in. high, 5 in. wide, and 12 in. long. A bug, starting at one corner of the box, crawls along the inside surface of the box to the opposite corner (i.e., to the one farthest away from the bug's corner). Assuming the bug travels along the shortest path possible, while staying on the surface of the box, how far does it travel?

(solution)