$\textbf{Running Dog}$

Joe and Mary walk towards each other from $1000$m apart at speeds of $1.20$m/s and $0.80$m/s, respectively. Joe's dog, starting at the same time as Joe, runs toward Mary at a speed of $2.50$m/s. When it meets Mary, the dog immediately turns back and run towards Joe at the same speed. When the dog meets Joe the next time, it turns back and run towards Mary at the same speed again. In another word, the dog runs between Joe and Mary back and forth until the two people meet. What is the total distance run by the dog?