It’s an important detail, because, if they’d felt no urgency, the one disciple, being friends with the other, would’ve slowed his pace so they could remain in each other’s company. For that is what friends do, when they are hurrying toward some destination, and the destination does not matter more to them than the fact that they are going to it together. Unless they are having a footrace, to see who is faster, which is not what these two were doing. No, it was merely because Peter was older, slower, and probably a little out of breath, that he was outrun by the other disciple, though you can be certain he was going as fast as he could.