Cambridge Maths 7 Chapter 7

336 33 6

Chapter 7 Time

7

Chapter

Time

What you will learn

ISBN: 9781107626973

7A

Units of time

7B

Working with time

7C

Using time zones

© David Greenwood et al. 2013

Cambridge University Press

337

NSW Syllabus for the Australian Curriculum Strand: Measurement and Geometry Substrand: TIME

Outcome A student performs calculations of time that involve mixed units, and interprets time zones. (MA4–13MG)

Luxor temple obelisk Thousands of years before the use of clocks and even the introduction of the Gregorian calendar, sundials sundials were used to tell the time during the day. Egyptian obelisks dating back to 3500 BC were some of the earliest sundials used. The two 3300-year-old twin obelisks, once marking the entrance of the Luxor temple in Egypt, are still standing s tanding today. One of them, however, was gifted to France and in 1836 was placed at the centre of Place de la Concorde in Paris, where it still s till stands.

ISBN: 9781107626973



338 33 8

Chapter 7 Time

t s e t e r P

1

2

3

How many: a hours in one day? c minutes in one hour? e months in one year?

b d f

What day is it: a 3 days after Tuesday? c 3 weeks after Wednesday?

b d

seconds in one minute? days in one week? days in one year (not a leap year)?

6 days before Sunday? 10 minutes after 11:55 p.m. Saturday?

Give the time, using a.m. or p.m., that matches these descriptions. a 2 hours after 3 p.m. b 1 hour before 2:45 a.m. c 6 hours before 10:37 a.m. d 4 hours after 4:49 p.m. e

1

1

hours after 2:30 p.m.

f

3

g 2 hours before 12:36 p.m.

h

5 hours after 9:14 a.m.

1

2

2

hours before 7:15 p.m.

4

Convert the following to the units shown in brackets. a 60 seconds (minutes) b 120 minutes (hours) c 49 days (weeks) d 6 hours (minutes)

5

Melissa watched two movies on the weekend. One lasted 1 hour 36 minutes and the other lasted 2 hours 19 minutes. a What was the total time Melissa spent watching movies, in hours and minutes? b What was the total time in minutes?

6

Write the following times as they would be displayed on a digital clock; e.g. 8:15. a 3 o’clock b half past 2 c a quarter to 6

ISBN: 9781107626973



Measurement and Geometry

7A

Units of time Time in minutes and seconds is based on the number 60. Other units of time, including the day and year, are defined by the rate at which the Earth spins on its axis and the time that the Earth takes to orbit the Sun. The origin of the units seconds and minutes dates back to the ancient Babylonians, who used a base 60 number system. The 24-hour day dates back to the ancient Egyptians, who described the day as 12 hours of day and 12 hours of night. Today, we use a.m. (ante meridiem, which is Latin for ‘before noon’) and p.m. post meridiem, which is Latin for ‘after noon’) to ( post represent the hours before and after noon (midday). During the rule of Julius Caesar, the ancient Romans introduced the solar calendar, which recognised that the Earth takes about 365

1 4

The Earth takes 1 year to orbit the Sun.

days to orbit the Sun. This gave

rise to the leap year, which includes one extra day (in February) every 4 years. The calendar we use today is called the Gregorian calendar. It was formally introduced by Pope Gregory XIII in 1582 and includes the 12 months, each with 30 or 31 days, except for February, February, which has 28 days or 29 days in a leap year. Number

1

2

3

4

5

6

7

8

9

10

11

12

Month

Jan

Feb

Mar

April

May

June

July

Aug

Sep

Oct

Nov

D ec

Days

31

28/29

31

30

31

30

31

31

30

31

30

31

Time after Christ ( ad) is now often referred to as the Common Era ( ce) and the time before Christ ( bc) is also referred to as Before the Common Era ( bce).

Let’s start: Knowledge of time Do you know the answers to these questions about time and the calendar? • When is the next leap year? • Why do we have a leap year? • Which months have 31 days? • Why are there different times in different countries or parts of a country? • What do bc (or bce) and ad (or ce) mean on time scales?

ISBN: 9781107626973



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s a e d i y e K

Chapter 7 Time

■ ■

■ ■

■

The standard unit of time is the second (s). Units of time include: – 1 minute (min) = 60 seconds (s) × 24 × 60 × 60 – 1 hour (h) = 60 minutes (min) day hour minute second – 1 day = 24 hours (h) ÷ 24 ÷ 60 ÷ 60 – 1 week = 7 days – 1 year = 12 months a.m. or p.m. is used to describe the 12 hours before and after noon (midday). 24-hour time shows the number of hours and minutes after midnight. – 0330 is 3:30 a.m. – 1530 is 3:30 p.m. DMS conversion: Most scientific and graphics calculators have a DMS (Degrees, Minutes and Seconds) button or function that converts time in fraction or decimal form to hours, minutes and seconds. – For example: 2.26 hours → 2° 15′ 36″ , meaning 2 hours, 15 minutes and 36 seconds.

Example 1 Converting units of time Convert these times to the units shown in brackets. a 3 days (minutes) b 30 months (years) SOLUTION

E X P L A N AT I O N

a

1 day = 24 hours 1 hour = 60 minutes

3 days = 3 × 24 h = 3 × 24 × 60 min = 4320 min

b 30 months = 30 ÷ 12 years = 2

1

There are 12 months in 1 year.

years

Example 2 Using 24-hour time Write these times using the system given in brackets. a 4:30 p.m. (24-hour time) b 1945 hours (a.m./p.m.) SOLUTION a

4:30 p.m. = 1200 + 0430 = 1630 hours

b 1945 hours = 7 7::45 p.m.

ISBN: 9781107626973


Since the time is p.m., add 12 hours to 0430 hours.

Since the time is after 1200 hours, subtract 12 hours.



341


Example 3 Converting to hours, minutes and seconds Convert the following to hours, minutes and seconds. a

Convert mentally

4

1 3

b

hours.

SOLUTION a

4

1 3

= 4 hours, 20

Use a calculator to convert 6.42 hours.

E X P L A N AT I O N 1

minutes

3

b 4.42 → 4°25′12″ ″ = = 4 hours,

of an hour is 20 minutes because

1

of 60 = 20.

3

Use the DMS bottom on your calculator. Ensure your calculator is in Degree mode.

25 minutes and 12 seconds

Exercise 7A

I N G RK I

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1

U

Which months of the year contain: a 28 or 29 days? b 30 days?

A R T

c 31 days?

From options A to F, match up the time units with the most appropriate description. a single heartbeat A 1 hour b 40 hours of work B 1 minute c duration of a university lecture C 1 day d bank term deposit D 1 week e 200-m run E 1 year f flight from Australia to the UK F 1 second

3

State whether you would multiply by 60 (M) or divide by 60 (D) when conve converting: rting: a hours to minutes b seconds to minutes c minutes to hours d minutes to seconds

4

Find the number of: a seconds in 2 minutes c hours in 120 minutes e hours in 3 days g weeks in 35 days

d f h

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L H E C A M A T I C

2

b

F

C

M

minutes in 180 seconds minutes in 4 hours days in 48 hours days in 40 weeks I N G R K I

W O

Example 1

5

U

Convert these times to the units shown in brackets. a 3 h (min) b 10.5 min (s) d 90 min (h) e 6 days (h) g 1 week (h) h 1 day (min) j 20 160 min (weeks) k 2 weeks (min) m 3.5 h (min) n 0.25 min (s) p 270 min (h) q 75 s (min)

ISBN: 9781107626973

M

c 240 s (min)

A R T

PS

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L H E C A M A T I C A

f

72 h (days) i 14 400 s (h) l 24 h (s) o 36 h (days) r 7200 s (h)


F

C


342 34 2

7A

Chapter 7 Time

I N G RK I

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x am am p e

Example 3a

6

Write these times, using the system shown in brackets. a 1:30 p.m. (24-hour) b 8:15 p.m. (24-hour) d 11:59 p.m. (24-hour) e 0630 hours (a.m./p.m.) g 1429 hours (a.m./p.m.) h 1938 hours (a.m./p.m.)

c 10:23 a.m. (24-hour) f i

Write each of these digital clock displays as a number of hours expressed as a decimal; e.g. 4:30 is 4.5 hours. a 1:30 b 4:45 c 7:15 d 3:20

8

Write these times in hours and minutes.

9

1

1

hours

b

4

d 6.5 hours

e

3.75 hours

2

2

4

hours

Round these times to the nearest hour. a 1:32 p.m. b 5:28 a.m.

c

1

c

1

f

9.25 hours

3

F

C

A R T

PS

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L H E C A M A T I C

1300 hours (a.m./p.m.) 2351 hours (a.m./p.m.)

7

a

x a mp mp e

U

M

hours

d 1749 hours

1219 hours

10 Use the DMS button/function on your calculator to convert the following to hours, minutes

and seconds. a 7.12 hours

b 2.28 hours

c

d 8.93 hours

3.05 hours

I N G RK I

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11 Marion reads the following times on an airport display panel. Re-write the times using a.m.

or p.m. a 0630

U

M

A R T

PS

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L H E C A M A T I C

b 1425

c 1927

12 When there are 365 days in a year, how many weeks are there in a year? Round your answer to

2 decimal places. 13 Assuming there are 365 days in a year and my birthday falls on a Wednesday this year, on what day

will my birthday fall in 2 years’ time?

ISBN: 9781107626973

F

C



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I N G RK I

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14 Explain why:

M

A R T

a

4.2 hours is 4 hours and 12 minutes . b 2 hours and 10 minutes is 2.16 hours To convert from hours to seconds, what single number do you multiply by? b To convert from days to minutes, what single number do you multiply by? c To convert from seconds to hours, what single number do you divide by? d To convert from minutes to days, what single number do you divide by?

16 Without the use of the DMS function on your calculator, but allowing the use of your calculator’s

basic functions, convert the following to hours, minutes and seconds. a 2.4 hours b 7.18 hours c 9.92 hours

Enrichment 17 There is a rich history associated with the way civilisations

have recorded time and with the development of today’s calendar. Use the internet as a research tool and write 5–10 points summarising this topic. You may want to include topics relating to: ■ the introduction of the Gregorian calendar ■ the number of days in the year and in a leap year ■ the lunar calendar some ancient methods of recording time ■ ■ the Roman influence on today’s calendar ■ the use of sundials.


PS

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L H A E M T I C A C

15 a

ISBN: 9781107626973

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344 34 4

7B

Chapter 7 Time

Working with time It is a common activity to make a calculation involving time. For example, working out the duration of a sporting event or show, finding a train’s time of arrival, using a timetable,, or estimating time durations for trade quotes timetable or cooking. These calculations may involve operations such as addition or subtraction, and the use of the different ways that time can be displayed.

Let’s start: Your mental strategy Mental strategies are helpful in working out the sums and differences associated with time. Try to work out the answer to these simple problems and then describe the mental strategy you used to your group or class. • A football match begins at 1:45 p.m. and finishes at 4:10 p.m. What is the duration of the match? • A train leaves the city station at 8:40 a.m. and arrives in town

2

1 2

hours later. At what time does

the train reach town? • The construction of the Great Pyramid of Giza began in 2560 bc. How old does that make the pyramid now?

s a e d i y e K

■

■

■

Mental strategies should be used to solve simple problems involving time. – The total time to build two models, which took 45 minutes and 55 minutes each, is 55 + 5 + 40 = 1 hour 40 minutes. – The time duration of a taxi ride beginning at 2:50 p.m. and ending at 3:35 p.m. is 35 + 10 = 45 minutes or 60 – 15 = 45 minutes. The bc and ad timeline is similar to a number line in that it extends in both directions, with 0 representing the birth of Christ. The time duration from 500 bc to 2000 ad is therefore 500 + 2000 = 2500 years. When solving problems to do with time, it may be helpful to use the same type of units. BC

2000

ISBN: 9781107626973

AD

1500

1000

500

0

500


1000

1500

2000



Example 4 Calculating time intervals Mentally calculate the time interval between these pairs of times. a 4:35 p.m. to 9:10 p.m. b 5 h 20 min min 20 s to 7 h 40 min min 10 s SOLUTION a


Time interval = 4 h + 25 min + 10 min = 4 h 35 min

b Time interval = 2 h + 20 min − 10 s = 2

There are 4 hours from 5 p.m. to 9 p.m., another 25 minutes before 5 p.m., and then 10 minutes after 9 p.m. 2 hours and 20 minutes after 5 h 20 min and 20 s is 10 seconds too many, so subtract 10 seconds. A calculator method might include entering 7 °40′10″ ″ − − 5°20′20″ , using the DMS button or °, ′ and ″ symbols.

h 19 min 50 s

Example 5 Using timetables Use this train timetable for Bathurst to Penrith to answer these questions. Station

a.m.

p.m.

Bathurst

7:11

2: 41

Lithgow

8:15

3: 45

Bell

8:32

4: 0 2

Mount Victoria

8:42

4: 13

Katoomba

8:57

4: 2 9

Springwood

9:29

5: 01

Penrith

9:54

5: 30

a

How long does it take to travel from: i Bathurst to Lithgow in the morning? ii Lithgow to Penrith in the morning? iii Bathurst to Penrith in the afternoon? b Luke travels from Lithgow to Bell in the morning and then from Bell to Katoomba in the afternoon. What is Luke’s total travel time? SOLUTION


a

8:15 is 1 hour plus 4 minutes after 7:11. 1 hour and 45 minutes takes 8:15 to 10:00, so subtract 6 minutes to get 9:54. 3 hours after 2:41 is 5:41, so subtract 11 minutes.

i ii iii

1 h 4 min 1 h + 45 min – 6 min = 1 h 39 min 3 h – 11 min = 2h 49 min

b 17 min + 27 min = 44 min

ISBN: 9781107626973

8:15 to 8:32 is 17 minutes, and 4:02 to 4:29 is 27 minutes. This gives a total of 44 minutes.



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346 34 6

Chapter 7 Time

Exercise 7B

I N G RK I

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1

U

State whether each of the following is true or false. a There are 60 seconds in 1 hour. b 12 noon is between morning and afternoon. c There are 35 minutes between 9:35 a.m. and 10:10 a.m. d There are 17 minutes between 2:43 p.m. and 3:10 p.m. e The total of 39 minutes and 21 minutes is 1 hour.

F

C

M

A R T

PS

Y

L

L H E C A M A T I C

2

What is the time difference between these times? a 12 noon and 6:30 p.m. b 12 midnight and 10:45 a.m. c 12 midnight and 4:20 p.m. d 11 a.m. and 3:30 p.m.

3

Add these time durations to give a total time. a 1 h 30 min and 2 h 30 min b 4 h 30 min and 1 h 30 min c 2 h 15 min and 1 h 15 min d 6 h 15 min and 2 h 30 min e 3 h 45 min and 1 h 30 min f 4 h 45 min and 2 h 45 min I N G RK I

W O

Example 4a

4

5

x am am p e

U

Mentally calculate the time interval between these pairs of times. a 2:40 a.m. to 4:45 a.m. b 4:20 p.m. to 6:30 p.m. c 1:50 p.m. to 5:55 p.m. d 12:07 p.m. to 2:18 p.m. e 6:40 a.m. to 8:30 a.m. f 1:30 a.m. to 5:10 a.m. g 10:35 p.m. to 11:22 p.m. h 3:25 a.m. to 6:19 a.m. i 6:18 a.m. to 9:04 a.m. j 7:51 p.m. to 11:37 p.m. Write the time for these descriptions. a 4 hours after 2:30 p.m. 1

b

10 hours before 7 p.m.

c

3 hours before 10 p.m.

d

7

e

6

f

1 hours before 1:25 p.m.

hours after 11:15 a.m.

M

A R T

hours after 9 a.m. 3

°, ′, ″

Calculate the time interval between these pairs of times. You may wish to use the DMS or buttons on your calculator. a 2 h 10 min 20 s to 4 h 20 min 30 s b 5 h 30 min 15 s to 8 h 45 min min 21 s c 9 h 46 min 13 s to 10 h 50 min 27 s d 1 h 30 min min 10 s to 2 h 25 min min 5 s e 6 h 43 min 28 s to 8 h 37 min 21 s f 4 h 51 min 42 s to 10 h 36 min 10 s

7

For each of the following, add the time durations to find the total time. Give your answers in hours, minutes and seconds. 2

1 4

hours and

c

3

1 2

hours

6.2 hours and 2.9 hours e 2 h 40 min 10 s and 1 h 10 min 18 s

ISBN: 9781107626973

1

2

b

5

d

0.3 hours and 4.2 hours 10 h 50 min 18 s and 2 h 30 min 12 s

f

3

hours and

2


3

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6

a

F

C

hours


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I N G RK I

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8

x a mp mp e

A ferry takes Selina from Cabarita to Circular Quay in 23 minutes and 28 seconds. The return trip takes 19 minutes and 13 seconds. What is Selina’s total travel time?

M

A R T

a.m.

p.m.

Fairfield

7:32

2:43

Granville

7:44

2:56

Auburn

7:48

2:59

Ashfield

8:01

3:12

Redfern

8:11

3:23

a

How long does it take to travel from: i Fairfield to Auburn Auburn in the morning? ii Granville to Redfern in the morning? iii Auburn to Redfern in the afternoon? iv Fairfield to Redfern in the afternoon? b Does it take longer to travel from Fairfield to Redfern in the morning or afternoon? c Jeremiah travels from Fairfield to Auburn in the morning and then from Auburn to Redfern in the afternoon. What is Jeremiah’s total travel time? 10 A scientist argues that dinosaurs died out

52 million years ago, whereas another says they died out 108 million years ago. What is the difference in their time estimates?

ISBN: 9781107626973


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9 Use this train timetable for Fairfield to Redfern to answer these questions. Station

F

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348 34 8

7B

Chapter 7 Time

I N G RK I

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11 Three essays are marked by a teacher. The first takes 4 minutes and 32 seconds to mark,

the second takes 7 minutes and 19 seconds, and the third takes 5 minutes and 37 seconds. What is the total time taken to complete marking the essays?

U

F

C

M

A R T

PS

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12 Adrian arrives at school at 8:09 a.m. and leaves at 3:37 p.m. How many hours and minutes is

Adrian at school? 13 On a flight to Europe, Janelle spends 8 hours and 36 minutes on a flight from Melbourne to Kuala

Lumpur, Malaysia, 2 hours and 20 minutes at the airport at Kuala Lumpur, and then 12 hours and 19 minutes on a flight to Geneva, Switzerland. What is Janelle’s total travel time?

I N G RK I

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14 To convert the speed 10 metres per second (m/s) to kilometres per hour (km/h), you must

M

A R T

15 Give a reason why airports and other workplaces might use a 24-hour display rather than

use a.m. or p.m. 16 Calculate a rent of $400 per week as a yearly amount. Assume 365 days in a year and show

your working.

Enrichment: Time challenges 17 A doctor earns $180 000 working 40 weeks per year, 5 days per week, 10 hours per day day.. What does

the doctor earn in each of these time periods? a per day b per hour c per minute d per second (in cents) 18 What is the angle between the hour and minute hands on an analogue clock at these times?

6:15 a.m.

b 4:55 p.m.

11

c 5:47 a.m.

12

1 2

10

3

9

4

8 7

6

5

19 Rex takes 3 hours to paint a standard-sized bedroom, whereas his mate Wilbur takes 4 hours

to paint a room of the same size. How long will it take to paint a standard-sized room if they work together?

ISBN: 9781107626973


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multiply by 3600 and divide by 1000 to give a factor of 3.6. Explain why.

a

F

C



7C

349

Using time zones During the 19th century, as railways and telecommunications developed, it became increasingly important to deal with the difference in local times. Standard time zones were introduced around the world, most of which are one-hourly deviations from standard time, which is taken to be the time in Greenwich, England (United Kingdom). Standard time or Greenwich Mean Time (GMT) is now called Coordinated Universal Time Time (UTC). In Australia, we use three main time zones: the Western, Central and Eastern Standard Time zones, which alter for daylight saving in some States and Territories.

Let’s start: Time zone discussion In groups or as a class, discuss what you know about Australian and international time t ime zones. You You may wish to t o include:

• time zones and time differences within Australia • UTC (or GMT) • daylight saving • the timing of telecasts of sporting events around the world.

■

The Earth is divided into 24 time zones (one for each hour).

– Twenty-four 15° lines of longitude divide the Earth into its time zones. Time zones also depend on a country’s borders and its proximity to other countries. (See map on pages 350–351 for details.)

– Time is based on the time in a place called Greenwich, United Kingdom, and this is called Coordinated Universal Time (UTC) or Greenwich Mean Time (GMT).

– Places east of Greenwich are ahead in time. – Places west of Greenwich are behind in time. ■

Australia has three time zones:

– Eastern Standard Time (EST), which is UTC plus 10 hours. – Central Standard Time (CST), which is UTC plus 9.5 hours. – Western Standard Time (WST), which is UTC plus 8 hours.

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Chapter 7 Time

11

10

9

8

7

6

5

4

6

3

4

2

1

0

0

GREENLAND 1

3

ALASKA 9

1

6

ICELAND

SW NORWAY K UNITED KINGDOM N GERMANY P L

CANADA 4 Q

IRELAND 3½

FRANCE 8

P

UNITED STATES R

5

6

7

ITALY

PORTUGAL SPAIN 1 MOROCCO

LIB

ALGERIA MEXICO

CUBA MAURITANIA

MALI

NIGER

o

C 1

NIGERIA

VENEZUELA COLUMBIA

D OF 5

4

PERU

BRAZIL ANG BOLIVIA

World cities key

NAMIBI J K L M N P Q R

Auckland Edinburgh Greenwich Johannesburg London New York Vancouver Washington, DC

3 CHILE

ARGENTINA

Sun 1:00

2:00

3:00

4:00

5:00

6:00

7:00

8:00

9:00

10:00

11:00

Sun 12:00

13:00

11

10

9

8

7

6

5

4

3

2

1

0

1

F Western Standard Time

Central Standard Time

Eastern Standard D Time

Northern Territory B Western Australia

A Adelaide B Alice Springs C Brisbane D Cairns E Canberra, ACT F Darwin G Hobart H Melbourne I Perth

ISBN: 9781107626973

AUSTRALIA 9½

Australian cities key I

Queensland

South Australia

C New South Wales

A

E

Victoria H

20:00

21:00

8

9


Tasmania

G

22:00

10



2

1

4

3

5

6

8

7

9

10

12 12 12

11

11

3

11 SWEDEN

12

9

FINLAND

5

AY 3

10

RUSSIA

7

9

4 8 4

RMANY POLAND UKRAINE

6

KAZAKHSTAN

10

MONGOLIA

ROMANIA ITALY TURKEY

GREECE

CHINA

SYRIA IRAQ LIBYA

EGYPT

AFGHANISTAN 4½ 5

IRAN 3½

9 NEPAL 5¾

PAKISTAN

SAUDI ARABIA

BURMA

INDIA IGER CHAD

THAILAND

SUDAN

1

RIA

6½

5½

4

JAPAN

8

2

PHILIPPINES

5½ ETHIOPIA MALAYSIA

SRI LANKA DEM. REP. OF THE CONGO

INDONESIA

TANZANIA

ANGOLA ZAMBIA MADAGASCAR

NAMIBIA

AUSTRALIA 3

M

SOUTH AFRICA

11½

9½

ZIMBABWE J

NEW ZEALAND

12¾ 5 13:00

14:00

15:00

16:00

17:00

18:00

19:00

1

2

3

4

5

6

7

20:00

21:00

8

9

22:00

10

23:00

11

Sun Sun Sun 24:00 20:00 1:00

12

12

11

NT QLD WA SA NSW VIC ACT

Daylight saving No daylight saving

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TAS



351

352 35 2

Chapter 7 Time

s a e d i y e K

Daylight saving is the practice of moving clocks forward, usually by one hour, to create more

■

daylight in the evening and less daylight in the morning. In some parts of Australia, daylight saving runs from the first Sunday in October to the first Sunday in April. The International Date Line separates one calendar day from the next. So crossing the date line

■

from west to east subtracts one day.

Example 6 Working with Australian time zones Use the Australian standard time zones map (on pages 350–351) to help with these questions. When it is 8:30 a.m. in New South Wales, what time is it in each of the following?

a

Queensland

b Northern Territory

c Western Australia

SOLUTION


a

Using standard time, NSW and Qld are in the same time zone.

8:30 a.m.

NT is UTC

b 8:00 a.m.

So NT is

c

6:30 a.m.

1 2

+ 9

1 2

hours, whereas NSW is UTC + 10 hours.

hour behind.

WA is UTC + 8 hours and so is 2 hours behind NSW.

Example 7 Using time zones Coordinated Universal Time (UTC) is based on the time in Greenwich, United Kingdom. Use the world time zone map (on pages 350–351) to answer the following.

a

When it is 2 p.m. UTC, find the time in these places.

i

France

ii China

iii Queensland

iv Alaska

b When it is 9:35 a.m. in New South Wales, Wales, Australia, find the time in these places. i

Alice Springs

ii Perth

iii London

iv central Greenland

SOLUTION


a

Use the time zone map to see that France is to the east of

i

2 p.m. + 1 hour = 3 p.m.

Greenwich and is in a zone that is 1 hour ahead.

ii

2 p.m. + 8 hours = 10 10 p.m.

From the time zone map, China is 8 hours ahead of Greenwich.

midnigh ightt iii 2 p.m. + 10 hours = 12 midn

Quee Qu eens nsla land nd use usess East Easter ern n Stan Standa dard rd Time Time,, which which is 10 10 hour hourss ahead of Greenwich.

iv 2 p.m. − 9 hours = 5 a. a.m.

Alaska is to the west of Greenwich, in a time zone that is 9 hours behind.

ISBN: 9781107626973



353


b i

9:35 a.m. – hour = 9:0 9:05 5 a.m. a.m.

Alic Al icee Spr Sprin ings gs us uses es Ce Cent ntra rall Sta Stand ndar ard d Tim Time, e, wh whic ich h is is

2

ii

behind Eastern Standard Time.

9:35 a.m. − 2 hours = 7:3 7:35 5 a.m. a.m.

2

hour

Pert Pe rth h use usess Wes Wester tern n Sta Stand ndar ard d Tim Time, e, whi which ch is is 2 hou hours rs be behin hind d Eastern Standard Time.

iii

iv

9:35 a.m. − 10 hours = 11:35 p.m.

UTC (time in Greenwich, United Kingdom) is 10 hours

(the day before)

behind EST.

9:35 a.m. − 13 hours = 8:35 p.m.

Central Greenland is 3 hours behind UTC in Greenwich,

(the day before)

so is 13 hours behind EST.

Exercise 7C 1

I N G RK I

W O U

Which Australian States and Territories use daylight saving time?

F

C

M

A R T

2

PS

Y

L

L H E C A M A T I C

front of Coordinated Universal Time (UTC) are these countries and a How many hours in front Australian States?

i

Victoria, Australia

iv Thailand

ii South Australia

iii Western Australia

v China

vi Egypt

b How many hours behind Coordinated Universal Time (UTC) are the following countries? i

ii

Iceland

iii Columbia 3

eastern Brazil

iv Peru

When it is 10 a.m. Monday in New Zealand, what day of the week is it in the USA? I N G R K I

W O

4

x am am p e

Use the Australian standard time zones map (on pages 350–351) to help answer the following. When it is 10 a.m. in New South Wales, Wales, what time is it in these States and Territories?

5

a

Victoria

b

South Australia

c

Tasmania

d

Northern Territory

e

Western Australia

f

The Australian Capital Territory (ACT)

U

M

A R T

it is 4:30 p.m. in Western Western Australia, what time is it in the following States?

x am am p e

a

6

b New South Wales

South Australia

c Tasmania

Use the time zone map (on pages 350–351) to find the time in the following places, when it is 10 a.m. UTC.

Example 7b

7

a

Spain

b Turkey

c

Tasmania

d Darwin

e

Argentina

f

g

Alaska

h Portugal

Peru

Use the time zone map (on pages 350–351) to find the time in these places, when it is 3:30 p.m. in i n New South Wales.

a

b Libya

c Sweden

d Perth

e

f

g Alice Springs

h New Zealand

United Kingdom

ISBN: 9781107626973

Japan


PS

Y

L

L H E C A M A T I C

Use the Australian standard time zones map (on pages 350–351) to help answer the following. When

a

F

C

central Greenland


354 35 4

7C

Chapter 7 Time

I N G RK I

W O U

8

9

What is the time difference between these pairs of places?

a

United Kingdom and Kazakhstan

b

South Australia and New Zealand

c

Queensland and Egypt

d

Peru and Angola (in Africa)

e

Mexico and Germany

F

C

M

A R T

PS

Y

L

L H E A C M A T I C

Rick in Wollongong, NSW wants to watch a soccer ma tch that is being televised at 2 p.m. in England (United Kingdom). What time will he need to switch on his television in Wollongong? (Use Eastern Standard Time.)

10 At the London Olympics a rowing race is scheduled to begin at 11:35 a.m. What time will this be in Broome, Western Australia?

11 A 2-hour football match starts at 2:30 p.m. Eastern Standard Time (EST) in Newcastle, NSW. NSW. What time will it be in the United Kingdom when the match finishes?

12 If the date is 29 March and it is 3 p.m. in Perth, what is the time and date in these places? a

Italy

b Alaska

c Chile RK I I N G

W O U

13 Use the daylight saving time zone map (on pages 350–351) to help answer the following. During

M

daylight saving time, when it is 9:30 a.m. in Sydney, what time is it in the following States?

a

Queensland

b Victoria

c

South Australia

F

C

A R T

d Western Australia

14 During daylight saving time, Alice drives from Kingscliff in New South Wales to the Gold Coast in Queensland. How will she need to adjust her wristwatch when she crosses the border?

15 Explain why Eastern Standard Time in Australia is 11 hours ahead of the United Kingdom for a proportion of the year.

16 Monty departs on a 20-hour flight from Brisbane to London, United Kingdom, at 5 p.m. on 20 April. Give the time and date of his arrival in London (ignoring UK daylight saving time).

17 Elsa departs on an 11-hour flight from Johannesburg, South Africa, to Perth at 6:30 a.m. on 25 October. Give the time and date of her arrival in Perth. (Note: South Africa does not use daylight saving time.)

Enrichment: Time anomalies You may wish to use the 18 There are a number of interesting anomalies associated with time zones. You internet to help explore these topics.

a

Usually, States and Territories to the east are ahead of those in the west. During daylight saving time, however, this is not true for all States in Australia. Can you find these States and explain why?

Wales but does not use the New South Wales time zone. Explore. b Broken Hill is in New South Wales

c

Does Lord Howe Island (part of New South Wales) Wales) use the same time as New South Wales Wales all year round? Discuss.

d Are there any other time zone anomalies in Australia or overseas that you can describe? ISBN: 9781107626973


PS

Y

L




1

Teaghan takes 7 hours to fly from Dubbo, New South Wales Wales to Esperance, Western Western Australia. She departs at 7 a.m. What is the time in Esperance when she arrives? (Use Australian standard time.)

2

Albert can dig a post hole in 6 minutes and Sue can dig a post hole in 8 minutes. How long will it take for them to dig one hole if they work together?

3

When it is a Tuesday on 25 October in a particular year, what day will it be on 25 October in the following year, if it is not a leap year?

4

The average time for five snails to complete a race is 2 min 30 s. Four of the snails’ race times are 2 min 20 s, 3 min, 2 min 10 s and 1 min 50 s. What is the fifth snail’s race time?

5

At a speedway, the yellow car completes a lap every 30 seconds and the blue car completes a lap every 50 seconds. If the cars both start at the same place, how long will it take for the blue car to ‘lap’ the yellow car?

ISBN: 9781107626973



355

s e g n e l l a h c d n a s e l z z u P

356 35 6

Chapter 7 Time

y r a m m u s r e t p a h C

Conversion × 60 × 24 × 60

24-hour time

day hour minute second ÷

24

÷

60

÷

9:26 a.m. is 0926 5:03 p.m. is 1703

60

Time zones UTC (Coordinated Universal Time) is the time in Greenwich, England (United Kingdom). - Countries to the east are ahead - Countries to the west are behind

DMS conversion

Time

1.47 hours → 1 h 28′ 12″

Australian time zones State/ Territory WA

Standard 8

+

9

SA

+

Tas.

+

Vic.

+

NSW

+

ACT

+

Qld

+

9

Finding duration 4:35 to 6:44 = 2 h + 9 min 6:19 to 8:07 = 2 h − 12 min = 1 h 48 min

+

1 2 1 2

1 + 9 2 1

10 2

+

10

+

10

+

10

+

10

+

10

+

ISBN: 9781107626973

Mental strategies

8

+

NT

Daylight saving

11

Addition 2 h 26 min 12s + 3 h 24 min + 56 s = 5 h + 50 min + 68 s = 5 h 51 min 8 s

11 11 11 10




Multiple-choice questions 1

The number of minutes in 3 hours is:

A 180 2

B 60

B 2.5

5

6

E 200

C 2

D 3.5

E 4

D 1426

E 1626

When written using 24-hour time, 4:26 p.m. is:

A 0626 4

D 300

How many years are there in 42 months?

A 2 3

C 90

Converting

B 1226 2

2 3

C 0426

hours to hours and minutes gives:

A 2 h 67 min

B 2 h 35 min

D 2 h 40 min

E 2 h 30 min

C 2 h 23 min

Converting 2.64 hours to hours, minutes and seconds gives:

A 2 h 40 min 12 s

B 2 h 38 min 24 s

D 2 h 30 min 10 s

E 2 h 60 min 4 s

C 3 h 4 min 0 s

The time taken to make and assemble two chairs is 3 hours 40 minutes and 15 seconds and 2 hours 38 minutes and 51 seconds. Hence, the total build time is:

7

A 5 h 58 min 6 s

B 6 h 20 min 6 s

D 6 h 19 min 66 s

E 6 h 18 min 6 s

The time interval from 3:36 a.m. to 4:27 a.m. is:

A 51 min 8

B 49 min

C 41 min

D 39 min

E 61 min

How many hours is Western Australia behind New South Wales during Australian Australian standard time?

A 5 9

C 6 h 19 min 6 s

B 4

C 3

D 2

E 1.5

If it is 12 noon during daylight saving time in South Australia, what time is it in Queensland?

A 2 p.m.

B 2:30 p.m.

C 1 p.m.

D 12:30 p.m.

E 11:30 a.m.

D 3 p.m.

E

10 When it is 4 a.m. UTC, the time in Sydney is: A 1:30 p.m.

B 1 p.m.

C 2 p.m.

3 a.m.

Short-answer questions 1

Convert these times to the units shown in brackets.

a

1

1 2

h (min)

d 3 weeks (days) 2

b 120 s (min)

c 48 h (days)

e

f

1 day (min)

1800 s (h)

Re-write these times, using the system shown in brackets.

a

4 a.m. (24-hour time)

b

3:30 p.m. (24-hour time)

c

7:19 p.m. (24-hour time)

d

0635 (a.m./p.m.)

e

1251 (a.m./p.m.)

f

2328 (a.m./p.m.)

ISBN: 9781107626973



357

358 35 8

Chapter 7 Time

3

Re-write these times, using hours and minutes.

a 4

3

1 2

hours

b

4

1 3

c

hours

d 1.75 hours

6.25 hours

Use the DMS button/function on your calculator to convert the following to hours, minutes and seconds.

a 5

3.6 hours

b 6.92 hours

c 11.44 hours

Margaret is catching a train leaving at 1330 in London and arriving at 1503 in York. York. What will be Margaret’ Margaret’ss travel time?

6

Calculate the time interval between these pairs of times. Give your answer in hours, minutes and seconds.

7

a

7:43 a.m. to 1:36 p.m.

b

2 h 30 min 10 s to 6 h 36 min 5 s

c

5 h 52 min 6 s to 7 h 51 min 7 s

d

0931 to 1309

Use this train timetable ti metable for Telarah to Newcastle to answer the following questions. S ta t i o n

a

a.m.

p.m.

Telarah

7:30

2:52

Metford

7:42

3:04

Sandgate

7:55

3:16

Hamilton

8:10

3:30

Newcastle

8:16

3:36

How long does it take to travel from:

i

Telarah to Sandgate in the morning?

ii

Metford to Newcastle in the morning?

iii Sandgate to Newcastle in the afternoon? iv Telarah to Newcastle in the afternoon? b Does it take longer to travel from Telarah to Newcastle in the morning or afternoon? c

Ashdi travels from Telarah to Sandgate in the morning, then from Sandgate to Newcastle in the afternoon. What is Ashdi’s total travel time?

ISBN: 9781107626973




8

Use the Australian time zone maps (on pages 350–351) to help answer these questions.

a

During Australian standard time it is 7:45 a.m. in South Australia. What time is it in:

i

ii

New South Wales?

Western Australia?

Wales. What time is it in: b During Australian daylight saving time it is 4:36 p.m. in New South Wales.

i 9

ii Queensland?

Western Australia?

An AFL match telecast begins at 2:10 p.m. Eastern Standard Time. At what time will someone in the Northern Territory need to switch on the television if they want to watch the game?

Extended-response question 1

Use the International time zone maps (on pages 350–351) to answer these questions.

a

When it is 11 a.m. UTC, state the time in:

i

Sydney

ii Ethiopia

iii Pakistan

b When it is 3:30 p.m. in New South Wales, state the time in: i c

Zimbabwe

ii China

iii Bolivia

When it is 6 a.m. Tuesday in New South Wales, Wales, state the day of the week in:

i

India

ii Canada

d Chris flies from Sydney, leaving at 8 a.m., and travels for 7 hours, arriving in Kuala Lumpur, Malaysia. What is the time in Kuala Lumpur when he arrives?

ISBN: 9781107626973



359

Cambridge Maths 7 Chapter 7

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