First we find the time for Logan.
Logan was in the game 1/5 of the time. Since the time of the game was 60 minutes, to calculate the minutes that Logan played, we multiply 1/5 by 60:
Logan was 12 minutes in the game.
Now we find the time for Joseph.
Joseph was in the game 5/9 of the 60 minutes. To find the time that Joseph was in the game, we multiply 5/9 by 60:
Joseph was in the game 33.33 minutes.
The difference in their times is:
Answer: 21.33 minutes