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Walking with a Slower Friend

by Herb Bailey and Dan Kalman

This article originally appeared in:
College Mathematics Journal
November, 2011

Subject classification(s): Calculus | Single Variable Calculus | Continuity | Differentiation
Applicable Course(s): 3.1 Mainstream Calculus I

Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to meet Sam to complete one segment of their journey. The authors determine Fay’s optimal path minimizing segment length, and thus maximizing the number of times they meet during the walk. Two solutions are given: one uses derivatives; the other uses only continuity.


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Capsule Course Topic(s):
One-Variable Calculus | Differentiation: General Applications
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