The document is a lesson on ratios, rates, proportions, speed, distance, time and average speed. It contains examples and exercises on calculating rates, costs, speed, distance, time and average speed using relevant formulas. Sample problems include calculating the rate of typing in words per minute, the cost of goods in ringgit per kilogram, speed given distance and time, distance given speed and time, time given distance and speed, and average speed over a journey involving multiple speeds.

1. Friday, January 25, 2013
RATIO RATE & PROPORTION
BY
AIRIL BIN AHMAD
AIRIL BIN AHMAD

2. Friday, January 25, 2013
RATE
A RATE EXPRESS A
RELATIONSHIP INVOLVING 2
QUANTITIES OF DIFFERENT
KINDS.
AIRIL BIN AHMAD

3. Friday, January 25, 2013
EXAMPLE 1
A typist types 1200 words in one hour. What is her rate of
typing in words per minute?
The rate = 1200 / 60 minute
= 20 words per minute
AIRIL BIN AHMAD

4. Friday, January 25, 2013
Exercise
1. Alvin paid RM 240 for a year’s road tax for his van. What
rate per month was charged?
2. Rohani types 900 words in one hour. What was her rate of
typing in words per minute?
3. Maslan paid RM 8460 as quit rent for his house for a year.
What rate per month was charged?
4. A man paid RM2400 rent for 4 months. What was the
rental rate per month?
5. RM 15.64 is charged for 68 units of electricity. What is the
rate in cent per unit?
AIRIL BIN AHMAD

5. Friday, January 25, 2013
Example 2
If a gram of banana costs 0.14 cent, find the cost of 1kg in
ringgit
1 gram = 0.14 cent
1kg or 1000gram = 0.14 x 1000
= 140 cent
= RM 1.40
AIRIL BIN AHMAD

6. Friday, January 25, 2013
Exercise
1. If a gram of chicken costs 0.5 cent, find the cost of 1kg in
ringgit.
2. Sabrina types 50 words in 1 hour. How many words can
she type in 3 hour?
3. A car travels 1.5 km in one minute. How far does it travel in
1 hour?
4. If a gram of fish costs 22cent, find the cost of 3kg in ringgit.
5. If a gram of durian costs 0.3 cent, find the costs of 5 kg in
ringgit.
AIRIL BIN AHMAD

7. Friday, January 25, 2013
Example 3
If 6 metres of silk cloth cost RM 72.90, find the cost of 15
metres
Solutions:
6 metres of silk cloth cost RM72.90
1 metres costs RM72.90 = RM 12.15
6
Therefore 15 metres cost RM12.15 x 15
= RM 182.25
AIRIL BIN AHMAD

8. Friday, January 25, 2013
Exercise
1. If 9 book of the same price cost RM78.75, what is the cost
of 24 such books?
2. A bus travels 720 km on 36 litre of petrol. How far can it go
on 25 litres of petrol?
3. If 13 litres of petrol costs RM16.25, what is the cost of 18
litres?
4. If 2.5 dozen exercise books costs RM36.00, find the costs
of 36 such exercise books?
5. A car traveling at a uniform speed travels a distance of 450
km in 6 hours. How far does it travel in 9 hours?
AIRIL BIN AHMAD

9. Friday, January 25, 2013
SPEED , DISTANCE & TIME
BY
AIRIL BIN AHMAD
AIRIL BIN AHMAD

10. Friday, January 25, 2013
SPEED , DISTANCE & TIME
FORMULA
D
S T
AIRIL BIN AHMAD

11. Friday, January 25, 2013
Example 1
Find the speed if:
Distance = 320 km, Time = 5 hours
Speed = 320 km
5 hours
= 64 km per hours
AIRIL BIN AHMAD

12. Friday, January 25, 2013
Exercise
Find the speed if:
1. Distance = 254 km, Time = 2 hours
2. Distance = 218 km, Time = 4 hours
3. Distance = 500 km, Time = 6 hours
4. Distance = 60 cm, Time = 1.5 sec
5. Distance = 500 m, Time = 200 min
AIRIL BIN AHMAD

13. Friday, January 25, 2013
Example 2
Find the distance if:
Speed = 320 km/h, Time = 5 hours
Distance = 320 km/h X 5 hours
= 1600 km
AIRIL BIN AHMAD

14. Friday, January 25, 2013
Exercise
Find the distance if:
1. Speed = 60 km/h , Time = 5 hours
2. Speed = 240 m/s , Time = 4 sec
3. Speed = 360 cm/m , Time = 2 min
4. Speed = 48 m/s , Time = 4 sec
AIRIL BIN AHMAD

15. Friday, January 25, 2013
Example 3
Find the time if:
Distance= 6400 km , Speed = 400 km/h
Time = 6400 km/h
400 km/h
= 16 hours
AIRIL BIN AHMAD

16. Friday, January 25, 2013
Exercise
Find the time if:
1.Distance = 60 cm, Speed = 3cm/s
2.Distance = 160 km, Speed = 40 km/m
3.Distance = 500 m, Speed = 25 m/m
4.Distance = 290 km, Speed = 10 km/h
5.Distance = 350 cm, Speed = 70 cm/s
AIRIL BIN AHMAD

17. Friday, January 25, 2013
SPEED , DISTANCE & TIME
FORMULA
D
S T
AIRIL BIN AHMAD

18. Friday, January 25, 2013
AVERAGE SPEED
BY
AIRIL BIN AHMAD
AIRIL BIN AHMAD

19. Friday, January 25, 2013
AVERAGE SPEED
FORMULA
D
S T
AIRIL BIN AHMAD

20. Friday, January 25, 2013
Example 1
A car travels at an average speed of
75km/h in 20 minutes and 90 km/h in
30 minutes. Calculate the average speed
of the car.
car.
1 hour/60min =75km
1 min = 75 = 1.25
60
20 min = 1.25 x 20 = 25 km
AIRIL BIN AHMAD

21. Friday, January 25, 2013
Example 1
1 hour/60min =90km
1 min = 90 = 1.5
60
30 min = 1.5 x 30 = 45 km
AIRIL BIN AHMAD

22. Friday, January 25, 2013
Example 1
Total distance = 25 km + 45 km = 70km
Total time = 20 min + 30 min= 50min
Average Speed = Distance = 70 km
Time 50 min
= 1.4 x 60 = 84 km/h
AIRIL BIN AHMAD

23. Friday, January 25, 2013
Exercise
1. A bus travels at an average speed of
90km/h in 30 minutes and 120 km/h in
20 minutes. Calculate the average speed
of the bus.
AIRIL BIN AHMAD

24. Friday, January 25, 2013
Exercise
2. A train travels at an average speed of
80km/h in 15 minutes and 96 km/h in
25 minutes. Calculate the average speed
of the train.
AIRIL BIN AHMAD

25. Friday, January 25, 2013
Exercise
3. A bus travels at an average speed of
100km/h in 30 minutes and 140 km/h in
20 minutes. Calculate the average speed
of the bus.
AIRIL BIN AHMAD

26. Friday, January 25, 2013
Exercise
4. Bakar cycles for 3 hours at an average
speed of 18 km/h and then walks for 5
hours at an average speed of 8km/h.
Find the average speed for the whole
journey.
AIRIL BIN AHMAD

27. Friday, January 25, 2013
Exercise
1
5. Khalid took 1 hours to travel 70 km
2
from his house to the Zoo Negara. On
his return journey, he took 30 minutes
less. Calculate his average speed (km/h)
for the whole journey.
AIRIL BIN AHMAD

28. Friday, January 25, 2013
Exercise
6. The diagrams shows the distances
between three taxi stands, P,Q and R.
P 140km Q 60km R
A taxi traveled from P to Q at an average
speed of 60 km/h and from Q to R at
90km/h.
Calculate its average speed for the
whole journeys.
AIRIL BIN AHMAD

29. Friday, January 25, 2013
Exercise
6. The diagrams shows the distances
between three taxi stands, P,Q and R.
P 140km Q 60km R
AIRIL BIN AHMAD

30. Friday, January 25, 2013
SPEED , DISTANCE & TIME
FORMULA
D
S T
AIRIL BIN AHMAD

31. Friday, January 25, 2013
ACCELERATION
BY
AIRIL BIN AHMAD
AIRIL BIN AHMAD

32. Friday, January 25, 2013
ACCELERATION
Formula
Acceleration = New speed – Old speed
Time
AIRIL BIN AHMAD

33. Friday, January 25, 2013
Example 1
A car accelerates from 75 km/h to 115km/h
in 5 seconds to overtake a lorry. Calculate
the acceleration in km/h per second.
Solutions:
Accelerations= New Speed – Old Speed
Time
= 115 km/h – 75km/h
5 seconds
= 40km/h = 8 km/h/s
5s AIRIL BIN AHMAD

34. Friday, January 25, 2013
Exercise
1. A van which is moving at a speed of 45 km/h
accelerates to 75 km/h in 2 minutes. Calculate the
acceleration in km/h/m.
2. A car is moving along a road at 12 m/s. It then
speeds up to 30 m/s in 5 seconds. What is the car
acceleration?
3. A van travels from rest and reaches 60 km/h in 10
minutes. Calculate the acceleration of the car in
km/h per minute.
AIRIL BIN AHMAD

35. Friday, January 25, 2013
DECELERATION
BY
AIRIL BIN AHMAD
AIRIL BIN AHMAD

36. Friday, January 25, 2013
DECELERATION
Formula
Deceleration = New distance – Old Distance
Time
AIRIL BIN AHMAD

37. Friday, January 25, 2013
Example 1
The speed of a car changes from 120 km/h
to 70km/h in 5 seconds. Calculate the
deceleration in km/h per second.
Solutions:
Deceleration= New Speed – Old Speed
Time
= 70 km/h – 120km/h
5 seconds
= -50km/h = -10 km/h/s= 10km/h/s
5s
AIRIL BIN AHMAD

38. Friday, January 25, 2013
Exercise
1. The speed of a bicycle changes from 20m/min to 15 m/min
in 0.4 seconds. Find the deceleration of the bicycle in
m/min/sec.
2. Johnny drives his car at a constant speed of 85km/h. Then
he slows his speed to 80km/h in 3 seconds. Calculate the
deceleration in km/h/s.
AIRIL BIN AHMAD