💡 Detailed Explanation
The correct choice is '間に合い' (from '間に合う' - to be in time for). Preceded by the particle 'に' and following the reason '急いで走った' (ran in a hurry), '間に合いました' is logically and grammatically correct. Sentence translation: 'Because I ran in a hurry, I was in time for the train.' '遅れ' (to be late) and '乗り遅れ' (to miss a train) would contradict running in a hurry to succeed.