As a math and science educator I subscribe to a number of professional periodicals. One of my favorites is THE PHYSICS TEACHER. I was excited to find the following problem in the September 2012 issue.

**Physics Challenge for Teachers and Students**

Boris Korsunsky, Column Editor

West High School, Weston, MA 02493

**A Futile Chase**

Two turtles, A and B are relaxing at the
water’s edge a distance

*d*apart. Then A begins to swim away from the shore. B gives chase, taking off at the same moment. During the chase A keeps swimming directly away from the shore while B keeps swimming directly towards A. The speeds of both turtles are the same.*Find the distance between A and B after a long time interval.*
As soon as I read this "challenge" problem I quickly decided not to pursue a purely mathematical solution but, instead, model the problem in Scratch. I couldn't resist the fun of making two sprites in the form of turtles and then animating both turtles according to the conditions stated in the problem!

Here is a diagram of the starting position for both turtles.

Here is a diagram of the starting position for both turtles.

The chase is

*futile*because turtle B will never catch turtle A. Why? Both turtles travel with the same velocity, they are not traveling towards each other, and they start the chase with a separation distance*d*. Still, the geometry of the situation guarantees that turtle B will get*closer*to turtle A. What's the closest turtle B gets to turtle A? In other words, what is*d*after a long time interval?
I wrote the Scratch scripts, varied the starting distance

If you would like to form your own conjecture, here's the link to my Scratch program you can download and play with.

*d*, looked at the separation distance when both turtles were traveling in the same direction, and formed a*conjecture.*Doing the math to prove my conjecture*seems pointless to me because I so strongly believe my conjecture to be true!*If you would like to form your own conjecture, here's the link to my Scratch program you can download and play with.

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