LAUSR

Abstract This paper uses the lens of a calculus student to examine different solutions to a weekly puzzler from the radio show Car Talk, hosted by Tom and Ray Magliozzi. The puzzler describes an automobile that is traveling 75 miles per hour and is 75 miles from its destination. The trip is completed by traveling 1 mile at 75 miles per hour, 1 mile at 74 miles per hour, etc., until the last mile is traveled at 1 mile per hour. The goal of the puzzler is to determine how long (if ever!) it takes to arrive at the destination. We describe a direct method and two approximations for solving the puzzler. The approximations incorporate rich concepts from calculus and ultimately use the Euler–Mascheroni constant. The three different solutions to the puzzler are framed around projects that would be appropriate for students in a first-year calculus sequence.