John Gill Commentary John 20:4

"And they ran both together: and the other disciple outran Peter, and came first to the tomb;" — John 20:4 (ASV)

So they ran both together
At first setting out, and for a while; not content to walk, they ran, being eagerly desirous to know the truth of things:

and that other disciple did outrun Peter, and came first to the
sepulchre ;
John was a younger man than Peter, and so more nimble, and swift of foot, and got to the sepulchre before him; and besides, had not that concern of mind to retard him, Peter might have; as, supposing Christ was risen, and he should see him, how he should be able to look him in the face, whom he had so shamefully denied.