19. (7 points) When Wang Ming is 300 meters away from home after school, his sister and the puppy run towards him at the same time. Wang Ming and his sister both run at a speed of 50 meters per minute, while the puppy runs at a speed of 200 meters per minute. The puppy meets Wang Ming and then keeps running back and forth between Wang Ming and his sister at the same speed. When Wang Ming and his sister are 10 meters apart, how many meters has the puppy run in total?
The time the puppy ran is equal to the time when Wang Ming and his sister are 10 meters apart, the puppy ran: $200 \times 2.9=580$ meters,

Answer: When Wang Ming and his sister are 10 meters apart, the puppy has run a total of 580 meters.