Cambridge Maths 7 Chapter 7

Chapter 7 Time336

Chapter TimeTime7What you will learnUnits of timeWorking with timeUsing time zones

7A7B7C

ISBN: 9781107626973 Photocopying is restricted under law and this material must not be transferred to another party

© David Greenwood et al. 2013 Cambridge University Press

luxor temple obeliskThousands of years before the use of clocks and even the introduction of the Gregorian calendar, 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 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 stands.

nSW Syllabus for the australian CurriculumStrand: Measurement and Geometry

Substrand: tiME

Outcome

A student performs calculations of time that involve mixed units, and interprets time zones.

(MA4–13MG)

337



338 Chapter 7 Time338

1 How many:

a hours in one day? b seconds in one minute?

c minutes in one hour? d days in one week?

e months in one year? f days in one year (not a leap year)?

2 What day is it:

a 3 days after Tuesday? b 6 days before Sunday?

c 3 weeks after Wednesday? d 10 minutes after 11:55 p.m. Saturday?

3 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 11

2 hours after 2:30 p.m. f 3

1

2 hours before 7:15 p.m.

g 2 hours before 12:36 p.m. h 5 hours after 9:14 a.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

pre-

test



Measurement and Geometry 339 339

units of timeTime in minutes and seconds is based on the number

60. Other units of time, including the day and year, are

defi ned 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

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 3651

4 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, 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 Dec

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 timeDo 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?

7A

The Earth takes 1 year to orbit the Sun.



Chapter 7 Time340

■■ The standard unit of time is the second (s).

■■ Units of time include:

– 1 minute (min) = 60 seconds (s)

– 1 hour (h) = 60 minutes (min)

– 1 day = 24 hours (h)

– 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 scientifi c 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.

×24

÷24

day hour

×60

÷60

minute

×60

÷60

secondKey

idea

s

Example 1 Converting units of time

Convert these times to the units shown in brackets.

a 3 days (minutes) b 30 months (years)

Solution Explanation

a 3 days = 3 × 24 h

= 3 × 24 × 60 min

= 4320 min

1 day = 24 hours

1 hour = 60 minutes

b 30 months = 30 ÷ 12 years

= 21

2 years

There are 12 months in 1 year.

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.)


a 4:30 p.m. = 1200 + 0430

= 1630 hours

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

b 1945 hours = 7:45 p.m. Since the time is after 1200 hours, subtract 12 hours.



Measurement and Geometry 341

Example 3 Converting to hours, minutes and seconds

Convert the following to hours, minutes and seconds.

a Convert mentally 41

3 hours. b Use a calculator to convert 6.42 hours.


a 41

3 = 4 hours, 20 minutes 1

3 of an hour is 20 minutes because

1

3 of 60 = 20.

b 4.42 → 4°25′12″ = 4 hours,

25 minutes and 12 seconds

Use the DMS bottom on your calculator. Ensure your

calculator is in Degree mode.

1 Which months of the year contain:

a 28 or 29 days? b 30 days? c 31 days?

2 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 fl ight from Australia to the UK F 1 second

3 State whether you would multiply by 60 (M) or divide by 60 (D) when converting:

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 b minutes in 180 seconds

c hours in 120 minutes d minutes in 4 hours

e hours in 3 days f days in 48 hours

g weeks in 35 days h days in 40 weeks

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5 Convert these times to the units shown in brackets.

a 3 h (min) b 10.5 min (s) c 240 s (min)

d 90 min (h) e 6 days (h) f 72 h (days)

g 1 week (h) h 1 day (min) i 14 400 s (h)

j 20 160 min (weeks) k 2 weeks (min) l 24 h (s)

m 3.5 h (min) n 0.25 min (s) o 36 h (days)

p 270 min (h) q 75 s (min) r 7200 s (h)

Example 1

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Chapter 7 Time342

6 Write these times, using the system shown in brackets.

a 1:30 p.m. (24-hour) b 8:15 p.m. (24-hour) c 10:23 a.m. (24-hour)

d 11:59 p.m. (24-hour) e 0630 hours (a.m./p.m.) f 1300 hours (a.m./p.m.)

g 1429 hours (a.m./p.m.) h 1938 hours (a.m./p.m.) i 2351 hours (a.m./p.m.)

7 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.

a 21

2hours b 4

1

4hours c 1

1

3hours

d 6.5 hours e 3.75 hours f 9.25 hours

9 Round these times to the nearest hour.

a 1:32 p.m. b 5:28 a.m. c 1219 hours d 1749 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 3.05 hours d 8.93 hours

Example 2

Example 3a

Example 3b

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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 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?

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7A




14 Explain why:

a 4.2 hours is 4 hours and 12 minutes

b 2 hours and 10 minutes is 2.16. hours

15 a 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

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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 infl uence on today’s calendar

■■ the use of sundials.



Chapter 7 Time344

Working with timeIt is a common activity to make a calculation involving

time. For example, working out the duration of a sporting

event or show, fi nding a train’s time of arrival, using a

timetable, or estimating time durations for trade quotes

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 strategyMental 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 fi nishes 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 21

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?

7B

■■ 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.

500500 10001000 15001500 20002000 0

BC AD

Key

idea

s




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 20 s to 7 h 40 min 10 s


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

= 4 h 35 min

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.

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

= 2 h 19 min 50 s

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.

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 4:02

Mount Victoria 8:42 4:13

Katoomba 8:57 4:29

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?


a i 1 h 4 min

ii 1 h + 45 min – 6 min = 1 h 39 min

iii 3 h – 11 min = 2h 49 min

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.

b 17 min + 27 min = 44 min 8:15 to 8:32 is 17 minutes, and 4:02 to 4:29 is 27 minutes.

This gives a total of 44 minutes.



Chapter 7 Time346

1 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.

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

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4 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.

5 Write the time for these descriptions.

a 4 hours after 2:30 p.m. b 10 hours before 7 p.m.

c 3 1

2 hours before 10 p.m. d 7

1

2 hours after 9 a.m.

e 6 1

4 hours after 11:15 a.m. f 1

3

4 hours before 1:25 p.m.

6 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 21 s

c 9 h 46 min 13 s to 10 h 50 min 27 s d 1 h 30 min 10 s to 2 h 25 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 fi nd the total time. Give your answers in hours,

minutes and seconds.

a 21

4 hours and 3

1

2 hours b 5

1

3 hours and 2

2

3 hours

c 6.2 hours and 2.9 hours d 0.3 hours and 4.2 hours

e 2 h 40 min 10 s and 1 h 10 min 18 s f 10 h 50 min 18 s and 2 h 30 min 12 s

Example 4a

Example 4b

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8 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?

9 Use this train timetable for Fairfi eld to Redfern to answer these questions.

Station a.m. p.m.

Fairfi eld 7:32 2:43

Granville 7:44 2:56

Auburn 7:48 2:59

Ashfi eld 8:01 3:12

Redfern 8:11 3:23


i Fairfi eld to Auburn in the morning?

ii Granville to Redfern in the morning?

iii Auburn to Redfern in the afternoon?

iv Fairfi eld to Redfern in the afternoon?

b Does it take longer to travel from Fairfi eld to Redfern

in the morning or afternoon?

c Jeremiah travels from Fairfi eld 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?

Example 5

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Chapter 7 Time348

11 Three essays are marked by a teacher. The fi rst 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?

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 fl ight to Europe, Janelle spends 8 hours and 36 minutes on a fl ight 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 fl ight to Geneva, Switzerland. What is Janelle’s total travel time?

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

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

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.

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Enrichment: time challenges

17 A doctor earns $180 000 working 40 weeks per year, 5 days per week, 10 hours per 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?

a 6:15 a.m. b 4:55 p.m. c 5:47 a.m.

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?

6

457

3

8

9

21011 12 1

7B




using time zonesDuring 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 (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 discussionIn groups or as a class, discuss what you know about Australian

and international time zones. You may wish to include:

• time zones and time differences within Australia

• UTC (or GMT)

• daylight saving

• the timing of telecasts of sporting events around the world.

7C

■■ 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.

Key

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Chapter 7 Time350

Sun1:00

Sun12:002:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 13:00

ANGOLA

ARGENTINA

BRAZIL

BOLIVIA

CANADA

CHILE

COLUMBIA

FRANCE

GERMANY

GREENLAND

ICELAND

IRELAND

ITALY

LIBYAALGERIA

MEXICO

PERU

PORTUGAL SPAIN

SWEDEN

CHADNIGERMALI

NAMIBIA

MAURITANIA

MOROCCO

UNITEDKINGDOM

NORWAY

NIGERIA

DEM. REP.OF THE CONGO

VENEZUELA

CUBA

UNITED STATES

ALASKA

GREECE

POLAND

o1

3 1

046

6

4

3½

568

71

54

3

9

J AucklandK EdinburghL GreenwichM JohannesburgN LondonP New YorkQ VancouverR Washington, DC

K

LN

PR

Q

World cities key

11 10 4 3 2 1 0 19 8 7 6 5

11 10 4 3 2 1 0 19 8 7 6 5

9½

820:00 21:00 22:00

9 10

WesternAustralia

SouthAustralia

NorthernTerritory

Queensland

New South Wales

Tasmania

EasternStandard

Time

CentralStandard

Time

WesternStandard

Time

A AdelaideB Alice SpringsC BrisbaneD CairnsE Canberra, ACTF DarwinG HobartH MelbourneI Perth

Australian cities key

AUSTRALIA

A

G

H

I

B

F

D

C

EVictoria




Sun24:00

Sun20:00

Sun1:0013:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

ANGOLA

CHINA

EGYPT

ETHIOPIA

FRANCE

GERMANY

INDIA

SRI LANKA

PAKISTAN

IRAQ

ITALY

JAPAN

KAZAKHSTAN

LIBYA

MALAYSIA

NEW ZEALAND

SOUTHAFRICA

SWEDEN

THAILAND

TURKEY

ZIMBABWE

SUDANCHADNIGER

NAMIBIA

TANZANIA

SAUDIARABIA

UNITEDKINGDOM

NORWAYFINLAND

IRAN

RUSSIA

MONGOLIA

MADAGASCAR

ZAMBIA

NIGERIA

DEM. REP.OF THE CONGO

AFGHANISTAN

NEPAL

BURMA

PHILIPPINES

INDONESIA

AUSTRALIA

GREECE

UKRAINEPOLAND

ROMANIA

SYRIA

1 2

4

3

3

4

4

4

3½4½ 5

5

6

7

5¾

5½

5½

6½

8

8

9

9

10

10

11 12

9½11½

12¾5

3

9

J

M

1 2 3 4 5 6 7 8 9 10 11 12 12 11

1 2 3 4 5 6 7 8 9 10 11 12 12 11

4 5 8 9 106 7

Daylight savingNo daylight saving

WA

NT

QLD

SANSW

ACTVIC

TAS



Chapter 7 Time352

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, Australia, find the time in these places.

i Alice Springs ii Perth iii London iv central Greenland


a i 2 p.m. + 1 hour = 3 p.m. Use the time zone map to see that France is to the east of

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

ii 2 p.m. + 8 hours = 10 p.m. From the time zone map, China is 8 hours ahead of

Greenwich.

iii 2 p.m. + 10 hours = 12 midnight Queensland uses Eastern Standard Time, which is 10 hours

ahead of Greenwich.

iv 2 p.m. - 9 hours = 5 a.m. Alaska is to the west of Greenwich, in a time zone that is

9 hours behind.

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


a 8:30 a.m. Using standard time, NSW and Qld are in the same time zone.

b 8:00 a.m. NT is UTC + 91

2 hours, whereas NSW is UTC + 10 hours.

So NT is 1

2 hour behind.

c 6:30 a.m. WA is UTC + 8 hours and so is 2 hours behind NSW.

■■ 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.Key

idea

s




1 Which Australian States and Territories use daylight saving time?

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

Australian States?

i Victoria, Australia ii South Australia iii Western Australia

iv Thailand v China vi Egypt

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

i Iceland ii eastern Brazil

iii Columbia iv Peru

3 When it is 10 a.m. Monday in New Zealand, what day of the week is it in the USA?

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4 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, what time is it in these States and Territories?

a Victoria b South Australia

c Tasmania d Northern Territory

e Western Australia f The Australian Capital Territory (ACT)

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

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

a South Australia b New South Wales c Tasmania

6 Use the time zone map (on pages 350–351) to fi nd the time in the following places, when it

is 10 a.m. UTC.

a Spain b Turkey c Tasmania d Darwin

e Argentina f Peru g Alaska h Portugal

7 Use the time zone map (on pages 350–351) to fi nd the time in these places, when it is

3:30 p.m. in New South Wales.

a United Kingdom b Libya c Sweden

d Perth e Japan f central Greenland

g Alice Springs h New Zealand

Example 6

Example 7a

Example 7b

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b i 9:35 a.m. – 1

2 hour = 9:05 a.m. Alice Springs uses Central Standard Time, which is

1

2 hour

behind Eastern Standard Time.

ii 9:35 a.m. - 2 hours = 7:35 a.m. Perth uses Western Standard Time, which is 2 hours behind

Eastern Standard Time.

iii 9:35 a.m. - 10 hours = 11:35 p.m.

(the day before)

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

behind EST.

iv 9:35 a.m. - 13 hours = 8:35 p.m.

(the day before)

Central Greenland is 3 hours behind UTC in Greenwich,

so is 13 hours behind EST.



Chapter 7 Time354

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

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 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 fl ight 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 fl ight 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.)

WORKING

MATHE M ATICALL

Y

U F

R PSC

Enrichment: time anomalies

18 There are a number of interesting anomalies associated with time zones. You may wish to use the

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 fi nd these States and explain

why?

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

c Does Lord Howe Island (part of New South Wales) use the same time as New South Wales all year

round? Discuss.

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

8 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

9 Rick in Wollongong, NSW wants to watch a soccer match 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. What time will it be in the

United Kingdom when the match fi nishes?

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

WORKINGM

ATHE M ATICALLY

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7C




1 Teaghan takes 7 hours to fl y from Dubbo, New South Wales to Esperance, 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 fi ve 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 fi fth 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?

puzz

les

and

chal

leng

es



Chapter 7 Time356

Ch

apte

r sum

mar

y

Finding duration4:35 to 6:44 = 2 h + 9 min6:19 to 8:07 = 2 h − 12 min

= 1 h 48 min

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

Mental strategies

Addition

Conversion

day hour minute second

÷ 24 ÷ 60 ÷ 60

× 24 × 60 × 60

DMS conversion1.47 hours →

1 h 28′ 12″

Time zones

Australian time zones

UTC (Coordinated UniversalTime) is the time inGreenwich, England (United Kingdom).- Countries to the east are ahead- Countries to the west are behind

State/Territory

WA

NT

SA

Tas.

Vic.

NSW

ACT

Qld

+ 8

+ 9

+ 9

+ 10

+ 10

+ 10

+ 10

+ 10

+ 8

+ 9

+ 10

+ 11

+ 11

+ 11

+ 11

+ 10

StandardDaylightsaving

1212

12

12

9:26 a.m. is 09265:03 p.m. is 1703

24-hour time

Time




Multiple-choice questions1 The number of minutes in 3 hours is:

a 180 B 60 C 90 D 300 E 200

2 How many years are there in 42 months?

a 2 B 2.5 C 2 D 3.5 E 4

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

a 0626 B 1226 C 0426 D 1426 E 1626

4 Converting 22

3 hours to hours and minutes gives:

a 2 h 67 min B 2 h 35 min C 2 h 23 min

D 2 h 40 min E 2 h 30 min

5 Converting 2.64 hours to hours, minutes and seconds gives:

a 2 h 40 min 12 s B 2 h 38 min 24 s C 3 h 4 min 0 s

D 2 h 30 min 10 s E 2 h 60 min 4 s

6 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:

a 5 h 58 min 6 s B 6 h 20 min 6 s C 6 h 19 min 6 s

D 6 h 19 min 66 s E 6 h 18 min 6 s

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

a 51 min B 49 min C 41 min D 39 min E 61 min

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

a 5 B 4 C 3 D 2 E 1.5

9 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.

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. D 3 p.m. E 3 a.m.

Short-answer questions1 Convert these times to the units shown in brackets.

a 11

2 h (min) b 120 s (min) c 48 h (days)

d 3 weeks (days) e 1 day (min) f 1800 s (h)

2 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.)



Chapter 7 Time358

3 Re-write these times, using hours and minutes.

a 31

2 hours b 4

1

3 hours c 6.25 hours d 1.75 hours

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

and seconds.

a 3.6 hours b 6.92 hours c 11.44 hours

5 Margaret is catching a train leaving at 1330 in

London and arriving at 1503 in York. What

will be Margaret’s travel time?

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

and seconds.

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

7 Use this train timetable for Telarah to Newcastle to answer the following questions.

Station 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


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?




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 New South Wales? ii Western Australia?

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

i Western Australia? ii Queensland?

9 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 question1 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 Zimbabwe ii China iii Bolivia

c When it is 6 a.m. Tuesday in New South 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?



Cambridge Maths 7 Chapter 7

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