Chapter 5.4, Problem 28MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinetly, and of uncovering pattern and structure.

Look before you leap. There is a fire in your high-rise dorm one night. You have to jump from a fourth-story window onto a circular fire safety net. While contemplating your chances of surviving the fall, you notice that the firefighters holding the net are rotating—going clockwise and then counterclockwise. You become mesmerized watching the motion of one firefighter’s red hat. It moves 1/4 of the way around the circle clockwise, then 1/3 of the way counterclockwise, then 1/2 of the way clockwise, then 1/8 of the way counterclockwise. How far has the firefighter in the red hat moved from his original position? Express your answer as a fraction of the distance around the circle clockwise or counterclockwise. (Historical aside: One of the most popular of the fire safety nets was called the Browder life net after Thomas Browder, who invented and patented the device in 1887. Wonder if he knew Felix Brouwer?)