TOKYO (AP) — Jade Carey traveled the world for a spot in the Olympics. Germany. Qatar. Azerbaijan. Australia.

A lot of long flights. A little bit of jet lag. One unrelenting vision of what could be possible.

She wasn't going to let a little thing like a sticky patch of carpet get in her way.

The 21-year-old American gymnast soared to gold in the women's floor exercise Monday night, her powerful and precise routine capping a roller-coaster 24 hours in which she narrowly avoided serious injury during the vault finals when her right foot caught just as she was preparing her entry.

Carey's score o...