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Secondary 2 Mathematics

Shatin Tsung Tsin Secondary School. Teaching Demonstration. Secondary 2 Mathematics. Solving Simultaneous Linear Equations on the Problems of Relative Motion. 140km. A. B. Basic term. Two cars A and B are 140km apart. Basic term. They travel towards each other. A. B.

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Secondary 2 Mathematics

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  1. Shatin Tsung Tsin Secondary School Teaching Demonstration Secondary 2 Mathematics

  2. Solving Simultaneous Linear Equations on the Problems of Relative Motion

  3. 140km A B Basic term Two cars A and B are 140km apart

  4. Basic term They travel towards each other A B They meet !

  5. Basic term They travel in the same direction B A Car A catches upwith Car B

  6. Speed The speed of a car is 50 km/h. The speed of a car is 50 km in one hour. The speed of another car is 100 m/min. The speed of another car is 100 m in one minute. Speed Formula: Distance = Speed×Time

  7. Learn how to set up equations to solve the problems

  8. Question 1 • A and B are 21 km apart • They walk towards each other • They will meet after 3 hours What are the speeds of A and B?

  9. km/h km/h : x km : y km A 21 km B Question 1 A and B are 21 km apart Set up an equation with 2 unknown speeds Walking towards each other Let x be A’s speed and y be B’s speed. They meet after 3 hours 3x km 3y km After 3 hours, how far will A walk ? 3x km After 3 hours, how far will B walk ? 3y km 3x + 3y = 21 How to equate the distances?

  10. B A 18 m Choice A • Question 2 • A and B are 18 m apart. Set up an equation with 2 unknown speeds. • Walking in the same direction A will catch up with B after 4 minutes.

  11. B A 18 m Choice B • Question 2 • A and B are 18 m apart. Set up an equation with 2 unknown speeds. • Walking in the same direction A will catch up with B after 4 minutes.

  12. : x m : y m B A 18 m • Question 2 • A and B are 18 m apart. Set up an equation with 2 unknown speeds. • Walking in the same direction Let x m/min be A’s speed and y m/min be B’s speed. A will catch up with B after 4 mins. 4x m 4y m How far will A walk after 4 minutes? 4x m How far will B walk after 4 minutes? 4y m 4x – 4y = 18 How to equate the distances?

  13. Variables • the speeds • the distance apart • the time

  14. Question 3 A car and a bicycle are a certain distance apart. Speed of the car : 65km/h Traveling towards each other, they meet in 2 hours. Two unknowns: • the distance apart -- x km • the speed of bicycle -- y km/h Do worksheet : Q.3

  15. x km Bicycle Car Question 3 Speed of the car : 65km/h Traveling towards each other, they meetafter 2 hours Let x km be the distance apart and y km/h be the speed of the bicycle. • Draw a diagram to show the situation. • (b) Set up an equation with the unknown distance and speed. They meet after 2 hours (65  2) km 2y km 65  2 + 2y = x

  16. Question 4 Two trains M and N are a certain distance apart. Speed of train N : 152 km/h Traveling in thesame direction, train N will catch up with train M in 2.5 hours. Do worksheet : Q.4

  17. x km Train N Train M Question 4 2 trains are a certain distance apart. Speed of train N : 152km/h Train N will catch upwith train M in 2.5 hours. Let x km be the distance apartand y km/h be the speed of train M. (a) Draw a diagram to show the situation. (b) Set up an equation with the unknown speed and time. After 2.5 hours 152  2.5 km 2.5y km 152  2.5 – 2.5y = x

  18. Question 5 Towards each other 480 m

  19. After 1 min Towards each other 480 m

  20. After 2 mins Towards each other 480 m

  21. Meet in 3 mins Towards each other 480 m

  22. Meet in 3 mins Towards each other 480 m Same direction 480 m

  23. Meet in 3 mins Towards each other 480 m Same direction After 2 mins 480 m

  24. Meet in 3 mins Towards each other 480 m Same direction After 4 mins 480 m

  25. Meet in 3 mins Towards each other 480 m Same direction After 6 mins 480 m

  26. Meet in 3 mins Towards each other Their speeds?? 480 m Same direction The dog catches up with the catin 8 mins 480 m

  27. 480 m 480 m Question 5 A dog and a cat are 480 m apart.  Traveling towards each other, they will meet in 3 minutes.  Traveling in the same direction,the dog will catch up with the cat in 8 mins. Let x m/min be the speed of the dog and y m/min be the speed of the cat. 3x m 3y m 3x + 3y = 480 8x m 8y m 8x – 8y = 480

  28. 3y m 3x m 8x m 480 m 8y m 480 m Solve the simultaneous linear equations: 3x + 3y = 480  (1) Do worksheet : Q. 6  (2) 8x – 8y = 480 From (1), 3(x + y) = 480 x + y = 160  (3) From (2), 8(x – y) = 480 x – y = 60  (4) (3) + (4): 2x = 220 x = 110 (3) – (4): 2y = 100 y = 50 The speed of the dog is 110 m/min and the speed of the cat is 50 m/min.

  29. 60 km 60 km Teddy Teddy Ann Ann Question 6 Ann and Teddy are 60 km apart. Their speeds ??  Cycling towards each other, they will meet in 1.5 hours.  Cycling in the same direction, Teddy will catch up with Ann in 4 hours. Let x km/h be the speed of Ann’s bicycle and y km/h be the speed of Teddy’s bicycle. 1.5y km 1.5x km 1.5x +1.5 y = 60 4y – 4x = 60 4y km 4x km

  30. Solve the simultaneous linear equations: 1.5x + 1.5y = 60  (1)  (2) 4y – 4x = 60 From (1), 1.5(x + y) = 60 x + y = 40  (3) From (2), 4(y – x) = 60 y – x = 15  (4) (3) + (4): 2y = 55 y = 27.5 (3) – (4): 2x = 25 x = 12.5 The speed of Ann’s bicycle is 12.5 km/h and the speed of Teddy’s bicycle is 27.5 km/h.

  31. Harder Problem 1 Kenneth and Betty are 200 km apart. If driving towards each other, they meet in 2 hours. If Betty starts driving at noon, and Kenneth starts in the same direction at 1 p.m., Kenneth will catch up with Betty at 6:45 p.m. Set up two equations with two unknown speeds.

  32. or Harder Problem Kenneth and Betty are 200 km apart. If driving towards each other, they meet in 2 hours. If Betty starts driving at noon, and Kenneth starts in the same direction at 1 p.m., Kenneth will catch up with Betty at 6:45 p.m. Set up two equations with two unknown speeds. Let x km/h be the speed of Kenneth’s car and y km/h be the speed of Betty’s bicycle. 2x + 2y = 200

  33. Harder Problem 2 (Circular motion) Susan and Peter are running on a 900m circular track outside the playground. Peter runs faster than Susan. If they start together and run in the same direction, Peter will catch up with Susan 6 minutes later. If they go in opposite directions, they will meet 1.2 minutes later. Set up two equations with two unknown speeds.

  34. Quick review • The key in setting up equations to solve problems of relative motion: Equate the distances !

  35. Use of Theory of Learning and Variation變易理論的運用 http://www.sttss.edu.hk/Mathematics/

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