This scenario happened to me (almost) yesterday in my tournament.
Hit my drive probably 240 yards but very close to OB, so I hit a provisional. My provisional only went about 150 yards but in the fairway. When we got to my provisional, we were unable to hit because the group in front was still in the way. So me and the guy in my cart zoomed ahead to see if we could find my first ball. We looked for probably 30 seconds before the green cleared so we went back and played my provisional, which I hit onto the green. When we drove up to the area in which my original had landed we searched for probably a minute and found it. The guy I was playing with said that I cannot use the original because I had already looked for it in the area it was found. I told him that I was allowed to play my provisional up to the point of where my original was thought to be and if I found it, I could use the original and pick up the provisional. Is that correct?
The reason I said almost happened yesterday, is because after we discussed/argued for a minute. Upon further inspection, it was not my ball. It was the exact same make, model, number, and blue mark on the ball, all it was missing was my red mark on the side. But it was enough to start the discussion, so I now I want to know what to do if that were to happen.