They both

(ο δυο). "The two" (Peter and the other disciple whom Jesus loved).Ran together

(ετρεχον ομου). Imperfect active of τρεχω. It was a race in eagerness to reach the tomb of Jesus.Outran Peter

(προεδραμεν ταχειον του Πετρου). Second aorist active indicative of προτρεχω, old verb, in N.T. only here and Luke 19:4, to run on before (ahead). "He ran ahead more swiftly (see John 13:27) than Peter" (ablative case after comparative adverb ταχειον, Koine for older θασσον).First

(πρωτος). Predicative nominative (not adverb προτον) and superlative used where only two involved. John won the race.

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Old Testament