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My Test

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Download Geometry Expressions Model for Meeting a Friend

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Adapted from New South Wales Higher School Certificate 2005 Mathematics examination, Question 10 (copyright held by NSW Board of Studies).

 

Two friends agree to meet during their lunch hour, but both are very busy and unsure whether they can make it.

They each agree to wait for '\(x\)' minutes and, if the other has not arrived, to leave.

What is their chance of meeting? Drag the WaitTime point to explore this problem.

 

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Let the unit square describe their lunch hour, and each point \((x, y)\) within that square represent each of our times of arriving.

Then the point (1/2, 2/3) would indicate that I arrived at 12:30, and my friend arrived at 12:40.

How then do the inequalities \(x - y <= t\) and \(y - x <= t\) describe our chance of meeting?

Points which lie within the shaded hexagon correspond to times of arrival for which we would meet. Points outside the polygon are times for which we would not meet. In fact, our chance of meeting for any wait time, \(x\), will correspond to the AREA of the shaded figure - and the moving point on the screen has coordinates \((x, area(x))\).

What is the algebraic model that best fits this situation? More simply, what is the formula for the area of the hexagon for any wait time, \(x\)?

Try building your own model for this problem using GXweb and use it to explore both the geometry and the algebra involved.

 

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