Two of your sister's former friends have gotten themselves lost in a storage room in some abandoned building. While your girlfriend managed to get one of them out, the other one apparently got turned around in the maze and is still lost
The lost individual happens to be a fugitive, and you've decided to head over to the building to capture them. As you reach the storage room in question, you notice a small map scribbled on the wall, which looks like this:
Luckily, it seems the fugitive didn't see the map, as she can only say that she's sitting at a T-junction
The fugitive, from what you've seen of them, seems rather unintelligent, so you feel you can anticipate her behaviour: Specifically, when you move the fugitive will run to the path closest to going directly away from your current position (based on her immediate surrounding when she starts running) and follow the path until she reaches another junction. She should be able to pinpoint where you are in the maze based on your footsteps, but you cannot determine where she is, where she started, or how far she travels. Based on previous experiences, you know that the fugitive can run 50% faster than you, and you also believe they are unlikely to stop or slow down to think. If the fugitive makes it to the exit, she will be able to escape and run away
Assuming these rules, is there a strategy to guarantee that you can catch her before she can escape?