The Problem

 

3.25 feet                                                                                                    

12 feet

  Walking through the park after a light rain, you spot a fading rainbow making a 180° arc over a small tree.

  The rainbow is a constant 12 feet wide, and the width is thinning at a rate of 1 inch per second.

 

  When the thickness of the rainbow is 3.25 feet, at what rate is the area of the rainbow decreasing?