1. SPEED Primary 6 Mathematics

2. Speed 2 Chapter Learning Outcomes At the end of this chapter, pupils will be able to:  Interpret speed as the distance travelled per unit of time  Calculate distance travelled given speed and time taken  Calculate average speed given distance travelled and time taken  Calculate time taken given speed and distance travelled  Solve word problems involving speed

3. Speed 3 For example, Speed is the distance travelled in one unit of time. Interpret speed as the distance travelled per unit of time  km/h  m/min  m/s  cm/s Speed can be expressed in different units. Speed involves 2 entities: Distance covered : Time taken Can you name other units that can be used to express speed?

4. Speed 4 Mr Ahmad is making a delivery. He is running late. How fast is he travelling? The speedometer shows that Mr Ahmad is travelling at 60 kilometres an hour. We say that the speed of the truck is 60 kilometres per hour. We write 60 kilometres per hour as 60 km/h. Interpret speed as the distance travelled per unit of time

5. Speed 5 Example 1 Interpret speed as the distance travelled per unit of time a)Ivy throws a paper aeroplane and it travels 4 m in 1 second. Its speed is 4 m/s. b) A ball rolls 90 cm in 1 minute. Its speed is. c) A flock of birds fly a distance of 70 km in 1 hour. Their speed is. a)A swimmer swims 30 m in 1 min. His speed is. 90 cm/min 70 km/h 30 m/min

6. Speed 6 Interpret speed as the distance travelled per unit of time Example 2 The distance between Town X and Town Y is 650 km. A motorist takes 13 hours to travel from Town X to Town Y. What is the speed of the motorist? Distance = 650 km Time = 13 h Speed = Distance ÷ Time = 650 ÷ 13 = 50 km/h The speed of the motorist is 50 km/h. D ST

7. Speed 7 Calculate distance travelled given speed and time taken Distance travelled = Speed × Time taken D ST

8. Speed 8 Example 1 A tortoise moves at a speed of 20 cm/h. At this speed, how far does it move in 2 h? Calculate distance travelled given speed and time taken Speed = 20 cm/h Time = 2 h Distance = Speed Time = 20 2 = 40 cm/h × D ST The snail moves 40 cm in 2 h.

9. Speed 9 Example 2 Shuling walks from her home to the market at a speed of 5 km/h. She takes 15 minutes to reach the market. What is the distance between her home and the market? Give your answer in km and m. Calculate distance travelled given speed and time taken Speed = 5 km/h Time = 15 min = h Distance = Speed Time The distance between her home and the market is 1 km 250 m. = km = 1 km 250 m

10. Speed 10 Calculate average speed given distance travelled and time taken We use the concept of average speed as things do not move at a constant/same speed all the time. What is Average Speed? Average speed is the average distance travelled per unit of time. Average speed = Total distance travelled ÷ Total time taken

11. Speed 11 Example 1 Sharifa takes 2 min to swim a distance of 50 m. Find her average speed in m/min. Average speed = Total distance ÷ Total time = 50 ÷ 2 = 25 m/min Sharifa’s average speed is 25 m/min. Calculate average speed given distance travelled and time taken

12. Speed 12 Example 2 Point W and Point X are 105 m apart. Point X and Point Y are 235 m apart. Gerald runs from Point W to Point X in 18 s. Then he runs from Point X to Point Y in 50 s. Find Gerald’s average speed for the distance from Point W to Point Y. W XY 105 m, 18 s235 m, 50 s ? m/s Total time taken = 18 + 50 = 68 s Total distance = 105 + 235 = 340 m Average speed = 340 ÷68 = 5 m/s Gerald’s average speed from Point W to Point Y is 5 m/s. Calculate average speed given distance travelled and time taken

13. Speed 13 Calculate time taken given speed and distance travelled D ST We can calculate the total time taken for a journey, given the speed and distance travelled. Total time taken =Total distance travelled ÷ Average speed

14. Speed 14 Example 1 = 3901 ÷ 765 ≈ 5 h It takes about 5 h to fly from Singapore to Perth. Time = Distance travelled ÷ Average speed The distance from Singapore to Perth is 3901 km. How long does an aeroplane with an average speed of 765 km/h take to fly from Singapore to Perth? Express your answer correct to the nearest hour. Calculate time taken given speed and distance travelled

15. Speed 15 Example 2 Car A and Car B are travelling to Town Z which is 252 km away. Car A travels at a speed of 60 km/h while Car B travels at a speed of 78 km/h. How long do Car A and Car B take to reach Town Z? Time taken by Car A = 252 ÷ 60 Time taken by Car B = 252 ÷ 78 Car A takes to reach Town Z. Car B takes to reach Town Z. Car A Car B Calculate time taken given speed and distance travelled

16. Speed 16 Example 1 Solving word problems involving Speed Miss Lim drove 240 km from Town A to Town B. She took 1.2 h for the first 100 km. For the remaining journey, she drove at an average speed of 70 km/h. What was her average speed for the whole journey? Town A X Town B 100 km, 1.2 h140 km, 70 km/h ? km/h Time taken for the next 140 km = 140 ÷ 70 = 2 h Time taken for the whole journey = 1.2 + 2 = 3.2 h Average speed for the whole journey = 240 ÷ 3.2 = 75 km/h Her average speed for the journey was 75 km/h.

17. Speed 17 Example 2 Solving word problems involving Speed a) Total time taken Sim Keong travelled of his journey in h. He travelled the remaining 116 km in h. a) Find the total time taken for the whole journey. b) Find the average speed for the whole journey Total time taken is h. b) 2 units  116 1 unit  116÷2 = 58 km 3 units  58 3 = 174 km Average speed = 174 ÷ = Average speed for the whole journey is h.

18. Speed 18 Solving word problems involving Speed Example 3 A scooterist took 5 h to travel from Town A to Town B at an average speed of 48 km/h. A car took 1 h less for the same journey. Find the average speed of the car. Town A Town B scooter 48 km/h, 5 h car ? km/h, 4 h Distance from Town A to Town B = 240 km Average speed of the car = 240÷4 = 60 km/h The average speed of the car is 60 km/h.

19. Speed 19 Reference - Textbooks Learning Outcomes Interpret speed as the distance travelled per unit of time 6B p.2–36A p.92 Calculate distance travelled given speed and time taken 6A p.3–66A p.93–95 Calculate average speed given distance travelled and time taken 6A p.6–196A p.95–96 Calculate time taken given speed and distance travelled 6A p.7–196A p.96 Solving word problems involving Speed6A p.20–276A p.97–102