A thin conveyor belt 15feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?
The correct answer is (15-pi)/ 2
the circumference covered by the belt of each circle = 1/2 (2 pi r/2) = 1/2 (2 pi 1/2) = pi/2
the total circumference of both circles covered by the belt = pi
the lenth of the distance belt that doesnot cover the circumferences of 2 circles = 15 - pi
so the distance between the centers of the circles = (15 - pi)/2
drawing a picture would be an easy way to understand why half of (15 - pi) is the distance between the centers of two circles.