Problem of the Week 1076

The Big Wheel

Imagine a gigantic solid wheel 100 miles in radius rolling along a flat surface at 60 miles per hour. You are behind a square window 6 feet on a side that lies on the surface:

 
Note: This diagram is not drawn to scale.

When the wheel rolls by, your window is darkened for a while. How much time (to the nearest second) elapses while the wheel is darkening all or part of your window?

Note: There are 5280 feet in one mile.

Source: An article by Neal Koblitz a long time ago. It might well be original with him.

© Copyright 2007 Stan Wagon. Reproduced with permission.