Dr. Sarah's While Visions of Roadrunners Danced in His Head

Wile E. Coyote
Philadelphia City and County Prisons
8201 State Road
Philadelphia, PA 19136

Dear Math 1010 Students:

I was stopped at a rest stop on 95 South when all of a sudden, the Roadrunner came speeding past me. I looked over and saw one of those automated speed checker signs which says "your speed is 120 miles/hour". So I knew that the Roadrunner was going fast! After waiting a little bit to decide what to do, I decided to try and catch him. I accelerated instantaneously (I'm good at that!) and kept going the same constant speed. I started my newly purchased Walmart velocitometer. My velocitometer works by observing a moving object and then tells you how fast you are going relative to that object, as a percentage. The velocitometer told me that I was travelling at 60% of the Roadrunner's speed. A cop stopped me and arrested me for excessive speeding, reckless driving and being a public menace. The Roadrunner was long gone when the cop hauled me off to jail. I don't think that I was speeding, but I'm no mathemagician, so this is where you come in.

  • Was I speeding? Why? Was I speeding excessively, driving recklessly and being a public menace?
  • What % should the velocitometer have read in order for me to catch the Roadrunner? Why?

    Help me - you're my only hope!
    Hungry as ever,
    Wile E. Coyote

    Author: Dr. Sarah J. Greenwald
    Comments: Read the above and think about how you would respond to Wile E. You may wish to write your work down on a scratch piece of paper.

    Be sure to explain not only your answers to the questions, and how you got them, but also explain why these are correct and make sense. For example, in answering the second question, you must explain in detail why your answer would have enabled Wile to catch the Roadrunner. To give evidence of deep mathematical understanding of the problem and solution, this means that you also must explore which other answers would or would not have allowed Wile E. to catch the Roadrunner and explain why. In addition, notice that Wile doesn't tell you what the speed limit was at the time that he was caught. We don't have all of the information that we need, as often happens when we try to solve real life problems, so you will need to address this issue.