Charles Ellicott 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: and the other disciple did outrun Peter. This is simply the result of the greater activity of John, who was probably younger than his companion. The thought that love outran doubt or fear, which has often been connected with the words, is not in harmony with the context, for Peter therefore went forth as soon as he heard Mary’s words (John 20:3); and Peter it was who first entered into the tomb (John 20:6).