We know that the average speed is simply the ratio of the total distance travelled over the total duration of the trip.
total distance = 500 mi + 380 mi + 600 mi
total distance = 1,480 mi
total time = 10 h + 8 h + 15 h
total time = 33 h
So the average speed is therefore:
average speed = 1,480 mi / 33 h
average speed = 44.85 mi / h