Which sentence is correct?
The quarterback threw the ball farthest than anyone else on the team.
The quarterback threw the ball farther than anyone else on the team.
The quarterback threw the ball further than anyone else on the team.
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How many quarterbacks are there? If there is one quarterback, he can throw far.
If there are two quarterbacks, one can throw farther than the other.
You need a comparison between three of a thing to use farthest (or biggest, tallest, smartest, etc.)
If everybody on the team is throwing the ball, then you'd be technically correct to say he threw the farthest (if he did).
The difference between farther and further is another matter.
As JamesWebster points out, the use of further instead of farther is widespread, which is OK, I guess.
The old rule about farther being a literal distance, whether a hundred feet or a million miles, and further being a figurative distance, as in "the furthest thing from my mind," allows for a more accurate expression. However, people generally know intuitively when you say "furthest thing from my mind" you are not talking about a literal distance. Moreover, "a little further down the road" is clearly a literal expression (in most instances), and people generally will not be surprised if you attach a literal distance to the expression, as in "oh, about a mile-and-a-half down the road."
It's dealer's choice as to how you roll in the farther/further locution. In formal writing, I think you are better off observing the difference between the literal and the figurative. I have a feeling, moreover, people might look askance if you say, "That's the farthest thing from my mind," though I could be wrong.