Education Technology

CAS your girl friend

Published on 06/09/2008

Activity Overview

In this activity, students find the time a man takes to catch a moving train. They solve the problem with and without using calculus.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 2 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:
    Without Calculus:

  • Examine the graph which shows the distances as a function of time if a man runs at constant velocity
  • Find the two points where the person can catch the train
  • Solve the system for any speed and find two solutions for time
  • Find the minimum speed to catch the train for which the two values for time are equal


  • Using Calculus:
  • Understand that the man is moving at minimum velocity and that the train has the same speed when he catches it
  • Find the position of the train door at a certain time and find the speed of the train at that time
  • Calculate the speed of the man running behind the train


  • Alternatively, find the equation of the tangent line as a first order Taylor polynomial
  • Solve the system for time
  • After the Activity

    Review student results.

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary