Puzzle Answer

We can use a table to solve this problem:



First, the first clue says that Dante finished before Annie so Dante is definitely not last and Annie is definitely not first. 

 Next, it says that Becca wasn't third so we can cross that box out. 

 Finally, it says that there were two runners between Annie and Carlos. That means that both Annie and Carlos couldn't have been 2nd or 3rd. Now we can see that Annie must be 4th.

 That makes Dante 3rd and Becca 2nd , leaving Carlos as 1st.

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