JC

 It sounds like you’re thinking of the scene in the Gospel of John after the resurrection.

In Gospel of John 20:3–4, it describes how two disciples ran to Jesus’ tomb:

• Simon Peter
• “the other disciple” (traditionally understood to be John the Apostle)

The text says that the “other disciple outran Peter and reached the tomb first.”

So yes — according to that passage, one disciple did run faster than the other, and it specifically notes that John arrived before Peter.