Jack is putting together gift boxes at a rate of 3 per hour in the first hour. Then Jill comes over and yells, “Work faster!” Jack, now nervous, works at the rate of only 2 gift boxes per hour for the next 2 hours. Then Alexandra comes to Jack and whispers, “The steadiest hand is capable of the divine.” Jack, calmer, then puts together 5 gift boxes in the fourth hour. What is the average rate at which Jack puts together gift boxes over the entire period?