The Boat-and-Ambulance Problem Revisited

Abstract

One characteristic of many contemporary mathematics classrooms is the use of nonroutine problems as the starting point and the focus of instruction. Accordingly, teachers are always searching for “big” problems that can engage students for extended periods of time, can facilitate their growth as problem solvers, and can further their understanding of mathematics. At this time of increased demand for these types of problems, modern technology has enhanced students' access to advanced mathematical topics and enlarged the pool of appropriate problems. This article is about one such problem, the boat-and-ambulance problem, from Connecting Mathematics (Froelich, Bartkovich, and Foerster 1991, pp. 54–55), in NCTM's Curriculum and Evaluation Standards for School Mathematics Addenda Series. Although this problem would traditionally be considered a calculus problem, we have used a noncalculus approach in three second-year algebra classes, as well as in two eighth-grade classes. It is well suited for students from advanced algebra through introductory calculus and furnishes a nice illustration of a function that is nonlinear.