A young skater aims to catch up with his friend, who is skateboarding at a constant speed of 3.8 m/s. Starting from rest, the young skater accelerates at 1.1 m/s² until reaching his maximum speed of 4.8 m/s, which he maintains thereafter. Calculate the distance the young skater has traveled by the time he catches up to his friend. Note that the two friends start skating from the same point.