A mile is nothing for a 3 year old to travel, and quickly. They can climb over fences too. We have 2.5 acres for my grandkids to wander around on, and play. We have a surveillance system. It's normal for them to go outside, and play. Not long ago, I told how the 3 & 5 year old "escaped" and went down the driveway to our neighbor's house, that trains dogs. They decided they wanted to visit the dogs, so off they went. It's about 1/4 mile to the end of the drive, to get to the neighbor's house. Fortunately, they had their walki-talkies, and I had mine on. I heard a man's voice coming over the walki-talkie. They managed to do 1/4 mile in the time it took me to use the restroom, refill my coffee cup, and get back outside. I know they can do a half mile faster than we adults can, because they go with us to check the mail. 1/4 mile each way.
In all the time they've been here, they've never left our yard without an adult before. We did not scream, and yell at them. No one had really told them they couldn't leave the yard without an adult being with them. We talked to them, and explained the rule. The kids were upset that they had scared when they left, and no adult knew where they were.