1. Overview of Problem Solving GES 131 Class 3

2. Problem: A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot?

3. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? Can I draw a picture of the problem?

4. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? Can I draw a picture of the problem?

5. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What is the goal of the problem?

6. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What is the goal of the problem? The time from when the student starts running until he catches the robot.

7. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What information do we have?

8. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What information do we have? Robot speed:.5 ft/sec Student speed: 5 ft/sec Robot has a 20 second head start.

9. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What additional information do we need?

10. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What additional information do we need? There is enough information here to solve the problem.

11. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What are the key unknown quantities?

12. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? What are the key unknown quantities? The time when the student catches the robot. The position of the student and robot at any time t.

13. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? Can I describe the problem in mathematical notation?

14. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? Can I describe the problem in mathematical notation? t = time since student started R(t) = distance traveled by robot at time t. R(t) =.5*(20+t) feet S(t) = distance traveled by student at time t. S(t) = 5t feet

15. Goal: The time when the student catches the robot. t = time since student started Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t What equations or conditions apply here?

16. Goal: The time when the student catches the robot. t = time since student started Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t What equations or conditions apply here? R(t) = S(t) describes when the student catches up with the robot.

17. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) What concepts might help to solve the problem?

18. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) What concepts might help to solve the problem? Solving a linear equation with one unknown variable. (t)

19. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) How can I solve this problem?

20. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) How can I solve this problem? Set R(t) = S(t). Solve for t to get the time when the student and robot have traveled the same distance. R(t) = S(t):.5(20+t) = 5t 4.5t = 10 t = 20/9 seconds.

21. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) t = 20/9 seconds. Does this look right?

22. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) t = 20/9 seconds. Does this look right? R(20/9) =.5(20 + 20/9) = 100/9 feet S(20/9) = 5*20/9 = 100/9 feet R(20/9) = S(20/9) Checks.

23. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) How long would it take the student to travel twice as far as the robot?

24. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student Catches up with Robot: S(t) = R(t) How long would it take the student to travel twice as far as the robot? S(t) = 2 R(t): 5 t = 2*.5*(20+t) 4t = 20 t = 5 seconds

25. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student travels twice as far as Robot: S(t) = 2 R(t) How long does it take the student to travel n times as far as the robot?

26. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student travels twice as far as Robot: S(t) = 2 R(t) How long does it take the student to travel n times as far as the robot? S(t) = n R(t): 5 t = n*.5*(20+t) (5-.5n)t = 10n t = 10n/(5-.5n) seconds.

27. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student travels n times as far as Robot: S(t) = n R(t) The original problem used what value for n?

28. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student travels n times as far as Robot: S(t) = n R(t) The original problem used what value for n? n = 1

29. Distance traveled by Robot: R(t) =.5*(20+t) Distance traveled by Student: S(t) = 5t Student travels n times as far as Robot: S(t) = n R(t) Solution: t = 10n/(5-.5n) seconds. It looks like n must be smaller than 10, or we get a negative solution for t. Why is that?

30. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? Is there an easier way to solve this problem?

31. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. How long in seconds will it take him to catch up with the robot? Is there an easier way to solve this problem? When the student starts, the robot has a 10 foot head start. The relative speed of the student with respect to the robot is 5 -.5 = 4.5 ft/sec. The gap will be closed in t = 10 ft /4.5 ft/sec = 20/9 seconds.

32. Exercise Determine which parts of the solution involved the following phases of problem solving. 1.Understand 2.Plan 3.Do 4.Reflect

33. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. Exercise: How long does it take the student to get within 2 feet of the robot?

34. A student building a mobile robot places it on the floor next to his chair. He puts his head on his desk to sleep. As he does so, he activates the robot, which immediately takes off and moves in a straight line at.5 ft/sec. 20 seconds later, he wakes up, sees the robot, and runs after it at 5 ft/sec. Exercise: How long does it take the student to get within 2 feet of the robot? S(t) = R(t) – 2: 5 t =.5*(20+t) – 2 4.5 t = 8 t = 16/9 seconds