Related rates at a shadow

A 2 m person walks away from a 6 m lamp at 1.5 m/s. Let x be lamp-to-person distance and y shadow length. Similar triangles give 6/(x+y)=2/y.

1. Simplify to y=x/2.
2. Differentiate with respect to time.
3. The tip moves at d(x+y)/dt.