"A mile a minute is 60 miles an hour, right? So when he was driving 60 miles an hour, he should've been keeping pace with her, right?"
He was keeping pace with her at 60 miles an hour. That's what he's saying: that she's still ahead. So at 60 miles an hour he can't reach her, because they have the same speed.
"If she was going a mile a minute and he was going 80 miles an hour, shouldn't he have passed her?"
He needs to reach her before he can *pass* her. Once he has reached her of course he will need to slow down in order not to pass her.