CLEARWATER, Fla. (AP) _ A couple who spent 21 hours floating in the Gulf of Mexico after getting knocked off the back of their boat was rescued by the Coast Guard on Monday.

While on a routine training mission, the pilot of a Coast Guard helicopter spotted a woman swimming about four miles off Sand Key and frantically waving for help. Minutes later, a Coast Guard boat found a man treading water nearby.

``They were very exhausted,'' Coast Guard Petty Officer Doug Schubert said. ``He stated two times he was ready to give up.''

Julie Parsons, 31, of Madeira Beach, and her boyfriend, Andrew Block, 31, of Largo, were dehydrated and slightly hypothermic but were not seriously injured, Coast Guard officials said.

Ms. Parsons was taken to Northside Hospital in St. Petersburg, and Block refused medical treatment.

The couple was about 16 miles offshore when their ordeal began Sunday afternoon. The boat was in gear and they were showering after going for a swim when they hit a wave and were knocked overboard.

Unable to catch up to the boat, which headed off with their dog aboard, they started swimming. By late Monday, the Coast Guard had still not found the boat.