Bk 2A Chapter 1 Rate and Ratio



1 Rate and Ratio

Review Exercise 1 (p. 1.3)

1. Walking speed of Annie’s grandmother[pic]

2. Average speed of Mr Lee’s car[pic]

3. Distance travelled by the bird[pic]

4. Time needed to travel 425 km[pic]

5. ∵ (ABC ( (PQR

∴ [pic]

[pic]

∴ [pic]

[pic]

6. ∵ (DEF ( (LMN

∴ [pic]

[pic]

∴ [pic]

[pic]

Activity

Activity 1.1 (p. 1.4)

1. (a) Distance that David can cycle in 1 hour

[pic]

(b) Distance that Mark can cycle in 1 hour

[pic]

2. Mark

Classwork

Classwork (p. 1.5)

(a) The required rate[pic]

(b) The required rate [pic]

(c) The required rate[pic]

(d) The required rate[pic]

Quick Practice

Quick Practice 1.1 (p. 1.6)

(a) Speed of the boat[pic]

(b) Speed of the boat[pic]

Quick Practice 1.2 (p. 1.6)

(a) Price of the ribbon[pic]

(b) Amount that Winnie needs to pay[pic]

Quick Practice 1.3 (p. 1.7)

(a) Jill’s rate of folding paper flowers[pic]

(b) Time needed to fold 50 pieces of paper flowers

[pic]

∴ Jill can finish 50 pieces of paper flowers for a party which will start in half an hour’s time.

Alternative Solution

Number of paper flowers folded in half an hour

[pic]

∴ Jill can finish 50 pieces of paper flowers for a party which will start in half an hour’s time.

Quick Practice 1.4 (p. 1.13)

(a) 18 : 24[pic]

(b) 0.36 : 0.9[pic]

(c) [pic][pic]

Alternative Solution

[pic]

(d) 150 g : 2 kg[pic]

Quick Practice 1.5 (p. 1.13)

∵ [pic]

∴ [pic]

Quick Practice 1.6 (p. 1.14)

(a) [pic]

∴ [pic]

(b) [pic]

∴ [pic]

Quick Practice 1.7 (p. 1.14)

(a) Number of red beans : total number of beans

[pic]

(b) Number of green beans[pic]

Number of green beans : total number of beans

[pic]

(c) Number of red beans : number of green beans

[pic]

Quick Practice 1.8 (p. 1.15)

Tom’s monthly expenditure[pic]

Tom’s monthly savings[pic]

Alternative Solution

Tom’s monthly savings[pic]

Quick Practice 1.9 (p. 1.15)

Fraction of the original piece of paper which is the area of the square[pic]

Let y cm2 be the area of the original piece of paper.

[pic]

∴ The area of the original piece of paper is 6 cm2.

Quick Practice 1.10 (p. 1.17)

(a) 0.6 : 0.4 : 1[pic]

(b) [pic]

[pic]

Quick Practice 1.11 (p. 1.17)

|(a) | |x |

|50 : 1 |20 cm |( 0.4 ) cm |

|1 : 25 000 |8 cm |( 2 ) km |

|[pic] |5 cm |( 1.5 ) km |

(b) For length on the scale drawing = 5 cm

and the actual length = 10 m = 1000 cm,

Scale[pic]

For length on the scale drawing = 2 cm

and the actual length = 1 mm = 0.1 cm,

Scale[pic]

For length on the scale drawing = 6 cm

and the actual length = 30 km = 3000 000 cm,

Scale[pic]

Hence,

|Length on the scale drawing |Actual |Scale |

| |length | |

|5 cm |10 m |1 : 200 |

|2 cm |1 mm |20 : 1 |

|6 cm |30 km |1 : 500 000 |

2. (a) Scale of the map

[pic]

(b) Let x cm be the distance between the two cities on the map.

∴ x cm : 18 km = 1 : 250 000

[pic]

∴ The distance between the two cities on the map is 7.2 cm.

(c) Let y km be the actual length of the river.

∴ 4.2 cm : y km = 1 : 250 000

[pic]

∴ The actual length of the river is 10.5 km.

3. (a) Actual length (width) of the study

[pic]

∴ The bench cannot be fit into the study.

(b) Actual area of the study[pic]

∴ Area of the study : area of the whole flat

[pic]

Exercise

Exercise 1A (p. 1.8)

Level 1

1. Eric’s running rate[pic]

2. Ellen’s answering rate[pic]

3. The worker’s wage[pic]

4. Weight of potato chips[pic]

5. Exchange rate for HKD and USD[pic]

6. Price of apples[pic]

7. The rent of the flat[pic]

8. Yvonne’s typing rate[pic]

9. Cost of the fish[pic]

10. The rate that the vehicles arrived at the traffic junction

[pic]

Level 2

11. For a 5 kg-pack of rice, price[pic]

For a 8 kg-pack of rice, price[pic]

∴ The 8 kg-pack of rice is cheaper.

12. (a) (i) Billy’s cycling speed[pic]

(ii) Bill’s cycling speed[pic]

(b) Joey’s cycling speed[pic]

∴ Joey’s cycling speed > Billy’s cycling speed

∴ Joey cycles faster than Billy.

Alternative Solution

Joey’s cycling speed[pic]

> 0.25 km/min

∴ Joey’s cycling speed > Billy’s cycling speed

∴ Joey cycles faster than Billy.

13. (a) (i) Price of barbecued pork in Singapore

[pic]

(ii) Price of barbecued pork in Hong Kong

[pic]

(b) Price of barbecued pork in Singapore

[pic]

∴ It is not cheaper to buy barbecued pork in Singapore.

Alternative Solution

Price of barbecued pork in Hong Kong

[pic]

∴ It is cheaper to buy barbecued pork in Hong Kong.

∴ It is not cheaper to buy barbecued pork in Singapore.

14. (a) Price of orange[pic]

(b) Price of one-and-a-half dozens oranges

[pic]

15. (a) The required exchange rate[pic]

(b) Amount of RMB that we can exchange

[pic]

16. (a) Mary’s reading speed[pic]

(b) Time needed by Mary to finish 66 pages[pic]

17. (a) Mr Fung’s running speed[pic]

(b) Distance ran by Mr Fung in 18 minutes

[pic]

∴ Mr Fung cannot finish a 3-km race in 18 minutes.

Alternative Solution

Time needed by Mr Fung to finish a 3-km race

[pic]

∴ Mr Fung cannot finish a 3-km race in 18 minutes.

18. (a) Henry’s average rate of saving money per month

[pic]

(b) Henry’s total saving between 1st January, 2009 to 31st March, 2009

[pic]

∴ Henry can afford to buy a toy worth $250.

19. (a) Mrs Lee’s hourly wage[pic]

(b) Let h hours be the time that Mrs Lee works per day.

[pic]

∴ Mrs Lee needs to work 10 hours per day.

Alternative Solution

The time that Mrs Lee needs to work per day

[pic]

20. (a) Petrol consumption rate of Peter’s car

[pic]

(b) Total petrol consumption for the whole journey

[pic]

∴ Peter cannot reach city B without refilling his car.

Alternative Solution

Distance travelled by Peter’s car using 20 L of petrol

[pic]

∴ Peter cannot reach city B without refilling his car.

21. (a) Kelvin’s running speed[pic]

(b) Kelvin’s walking speed[pic]

(c) (i) Total distance travelled by Kelvin

[pic]

Total time taken

[pic]

(ii) Kelvin’s average speed[pic]

22. (a) (i) Time taken by Mary[pic]

Time taken by Ann[pic]

(ii) [pic]

(b) (i) Distance travelled by Peter[pic]

Distance travelled by Mary[pic]

(ii) [pic]

∵ [pic]

∴ Peter will meet Mary at 12:24 p.m.

Exercise 1B (p. 1.21)

Level 1

1. (a) 48 : 72[pic]

(b) 0.2 : 0.8[pic]

(c) 1.5 : 0.45[pic]

2. (a) [pic][pic]

(b) [pic]

(c) [pic]

3. (a) 42 days : 2 weeks[pic]

Alternative Solution

42 days : 2 weeks[pic]

(b) 1.8 km : 600 m[pic]

(c) 25 min : 900 s[pic]

4. (a) Number of pencils : number of ball pens

[pic]

(b) Area of the blue regions : area of the yellow regions

[pic]

5. (a) 3 : 9 : 15[pic]

(b) [pic][pic]

6. (a) ∵ [pic]

∴ [pic]

(b) ∵ [pic]

∴ [pic]

7. (a) [pic]

∴ [pic]

(b) [pic]

∴ [pic]

(c) [pic]

∴ [pic]

|8. |(a) | |x |

|3 |1 |6 |4 |

|3 |2 |5 |3 |

|3 |3 |4 |2 |

|3 |4 |3 |1 |

|3 |5 |2 |0 |

|4 |1 |5 |9 |

|4 |2 |4 |8 |

|4 |3 |3 |7 |

|4 |4 |2 |6 |

|4 |5 |1 |5 |

|5 |1 |4 |14 |

|5 |2 |3 |13 |

|5 |3 |2 |12 |

|5 |4 |1 |11 |

|6 |2 |2 |18 |

|6 |3 |1 |17 |

(Accept any two continued ratios from the above table.)

Challenging Questions (p. 1.41)

1. (a) (i) Amount of inheritance obtains by the eldest son

[pic]

(ii) Amount of inheritance obtains by the eldest son

[pic]

(b) Let Mr Chan passes away k years later.

Amount of inheritance obtains by the eldest son

[pic]

Amount of inheritance obtains by the youngest son

[pic]

Hence,

[pic]

∴ The age of the second son when Mr Chan passed away is 21 + 12, that is 33.

2. To complete the job alone,

A’s working rate[pic]

B’s working rate[pic]

C’s working rate[pic]

Besides,

A’s working days : B’s working days[pic]

B’s working days : C’s working days[pic]

A’s working days : B’s working days : C’s working days

[pic]

Let y be the total number of working days for completing the job.

The part of job completed by A[pic]

The part of job completed by B[pic]

The part of job completed by C [pic]

∴ [pic]

∴ It takes 20 working days to complete the job.

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