I’ve been fascinated recently with questions that are difficult, but don’t require advanced mathematics. I’ve also been fascinated with questions that *require* algebraic thinking, as opposed to arithmetic thinking. Here is one that I think fits the bill, inspired by a recent walk through the airport:

You walk onto a moving walkway in an airport. There is a person already standing ahead of you on the walkway. What information would you need to determine if you will catch the person before reaching the end of the walkway, and how would you use the information to answer the question.

Sequel: The person in front of you has several pieces of luggage, and you won’t be able to pass them on the moving walkway. What information would you need to determine if it will be faster to walk next to the moving walkway, and how would you use that information to answer the question?

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howardat58I think this can be done with arithmetic, ie calculations with the numbers, using

time taken = distance divided by speed

but if you want to know at which distance from the end you meet the other person then a bit of algebra could come in handy. (or how long before you catch up with them)

KristyOne thing that is important to remember is that there are always multiple ways to approach a problem. A good task is one that has no clear direction of how to approach the problem, ie. “Create an equation comparing the rate… blah blah blah.” Even if it can be solved using arithmetic, I always tell my students “You’ve been using algebra since you were 5. Sometimes you just skip the equation part.”