16. (3 points) Wang Lei and her sister walk from home to the gym to play badminton. It is known that her sister walks 20 meters more per minute than Wang Lei. After 25 minutes, her sister arrives at the gym. At this point, her sister realizes she forgot the racket and immediately returns home along the same route to get it. She meets Wang Lei 300 meters away from the gym. What is the distance from Wang Lei's home to the gym in meters? $\qquad$ meters.
16. (3 points) Wang Lei and her sister walk from home to the gym to play badminton. It is known that her sister walks 20 meters more per minute than Wang Lei. After 25 minutes, her sister arrives at the gym. At this point, her sister realizes she has forgotten the racket and immediately returns along the original path to get it. She meets Wang Lei 300 meters away from the gym. What is the distance from Wang Lei's home to the gym? $\qquad$ meters.

【Analysis】When they meet 300 meters away from the gym, the distance difference between Wang Lei and her sister is $300 \times 2=600$ meters. Since her sister walks 20 meters more per minute than Wang Lei, the time they have been walking when they meet is $\frac{600}{20}=30$ minutes. Then, we can find the time it takes for her sister to walk 300 meters, and thus her speed, which allows us to determine the distance from Wang Lei's home to the gym.

【Solution】Solution: When they meet 300 meters away from the gym, the distance difference between Wang Lei and her sister is $300 \times 2=600$ (meters), the time they have been walking when they meet $=\frac{600}{20}=30$ (minutes),
The time it takes for her sister to walk 300 meters back $=30-25=5$ (minutes), her sister's speed $=\frac{300}{5}=60$ (meters/minute),
The distance from Wang Lei's home to the gym $=60 \times 25=1500$ (meters)
Answer: The distance from Wang Lei's home to the gym is 1500 meters.
Therefore, the answer is: 1500.
【Comment】This problem tests the concept of a meeting problem. The key is to be able to determine the time they have been walking when they meet based on the distance difference between them.