## Math Forum - Problem of the Week

### Runners

Use this applet from NCTM's Electronic Examples, Principles and Standards for School Mathematics to explore:

[Note: Before using the applet, orient the boy and girl so that they are both facing the tree. You may need to click on the icon of the boy or the girl to reverse his/her starting direction. See the "Instructions for using the applet" below.]

Questions:

1. Place the boy at starting position 25 and the girl at 0. Adjust the length of their strides so that they reach the tree at the same time. What are the step sizes? How much time did their trips take? Are these the only step sizes and times possible? Please explain.

2. Place the girl at 0. Set her step size to 5 and the boy's to 2. Where do you have to start the boy so that they finish at the same time? How long did their trips take?

3. Based on your answers to (a) and (b), explain how a runner's step size helps you predict the time she/he will take to run the full distance.

Instructions for using the applet:

• Set a starting position for each runner by dragging his or her icon along the tracks.

• Make sure both runners are facing the tree. Change the direction a runner faces by clicking once on the runner's icon.

• Set a step size for each runner by clicking on the Arrow Up or Arrow Down buttons in the lower left.

• Click on an icon for either runner in the lower left to turn it on/off.
 Play. Runs the simulation from current position. Pause. Press Play to resume. Reset. Returns runners to their previous positions.

Use the submit link below to get hints and also chances to revise.

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