It took my brother three minutes to reach the school gate and three minutes to return. At this time, my sister walked 360 meters. At this time, the two started at the same time, and my brother had to walk 360 meters more than my sister to catch up.

It is known that my brother walks 360-60=300 meters more than my sister every minute.

Then 360/300= 1.2 minutes.

At this time, my brother walked 360* 1.2=432 meters from home and caught up with his sister at 648 meters away from school.