Meeting a Friend
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 "t" minutes and, if the other has not arrived, to leave.
What is their chance of meeting? Drag the point X to explore this problem.
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?
What is the algebraic model that best fits this situation?
Drag the point X to find the probability of meeting within a 15 minute wait time.
Now find the length of the wait time required for a probability of 80%?
- Build an algebraic model for the chance of meeting by defining the following function:
Steve Arnold, 2018, Created with GeoGebra
This problem may also be modelled using CabriJr on the TI-83/84 series calculator. Click on the graphic below to download the file and try it yourself!
Try having students work in pairs: one generating data points using the CabriJr model and the partner entering these into lists to plot and then to help build their algebraic model!
Just wait until you try this with TI-nspire CAS!
And you may want to have a look at Geometry Expression.
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