Solution: Let the brother's speed be V, then the brother's speed is 2v and the time is T 。

(1) When the elder brother is behind the younger brother, 2vt-3=vt- 1, vt=2, 2vt=4.

(2) When the elder brother is in front of the younger brother, 2vt-vt=3+ 1, vt=4, 2vt=8.

When my brother runs 4 meters or 8 meters, the distance between them is 1 meter.