I'd GUESS a few thousand years, possibly as much as ten or twelve thousand. After 60 million years, all that would be left would be petrified material.
So your guess is what, that this T-Rex was alive 10-12 thousand years ago ?
If you are taking the creationist side, then we have no possible yardstick to measure 60 million years - nothing whatsover has existed that long. And everything that IS fossilized occured with in that time span also, so it does not take that long.
If you are taking the evolutionist side, then T-Rexs existed basically unchanged for 60 million years untill just recently.