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## The Sign Says: Walk Don't Run!

Twin sisters, Polly Dent and Pepso Dent, were going home from school. Assume that the twins have the same walking rate and the same running rate, and both remain constant.

On the way home, Polly walks half the way and runs the rest of the way. However, trying to be different yet the same, Pepso runs half of the time and walks the rest of the way.

Who gets home first?

Hint: Some initial options

• Set up equations to represent the situation
• Make some assumed values for rates, times, etc.
• Graph the problem
• Think-out a solution!

Solution Commentary: If you tried the three options, you should learn that the equations get messy, the assumed values help clarify, the graph makes a solution jump out at you, and the "think-out" process should make you say "It is obvious that....!"

If these comments do not make sense, go back and try each of the four initial options...but make sure that you do them correctly.

J.S. (Meridian) wrote: "You know I'm a sucker for this kind of thing, so you should be aware that I can't help myself...I'm sure there is an algebraic solution and I will do that, because it's what I do. However, it seems to me that if one of them runs half the time and walks half the time, then she shall run more than half the distance. That means she shall finish faster than her more tired sibling....It may turn out that other things about the problem might pop out when I work out the algebra, which could lead to some thoughts about "What is mathematics for?"