UNCORRECTEDSAMPLEPAGES
7A Unitsoftime
7B Latitudeandlongitude
7C Timezones
7D Timedifferenceusingtimezones
7E Timedifferenceusinglongitudes
NSWSyllabus
Inthischapter,astudent:
•Developsunderstandingandfluencyin mathematicsthroughexploringand connectingmathematicalconcepts, choosingandapplyingmathematical techniquestosolveproblems,and communicatingtheirthinkingand reasoningcoherentlyandclearly (MAO-WM-01)
•Solvesproblemsinvolvingtimeand locationinpracticalcontexts (MST-11-06)
©NSWEducationStandardsAuthority
Onlineresources
Ahostofadditionalonlineresourcesare includedaspartofyourInteractive Textbook,includingHOTmathscontent, videodemonstrationsofallworked examples,auto-markedquizzesandmuch more.
7A
Unitsoftime
Learningintentions
• Touseandunderstandtheconventionsof12-hourand24-hourtime
• Toconvertbetweenthecommonlyusedunitsoftime
• Toperformcalculationsandsolveproblemsinvolvingtime
Past,presentandfuturelearning
• Someoftheseconceptsmaybenewtostudents
• ThisisaYear11topicwhichisnotrepeatedorextendedinYear12
• QuestionsabouttimeregularlyappearinHSCExaminations
Timeistheongoing sequenceofeventstaking place:thepast,presentand future.Wemeasuretime usingseconds,minutes, hours,days,weeks,months andyears.Oneyearis thetimeittakesEarthto travelaroundtheSun. Thisisapproximately 365 1 4 days.Thereare 30daysinSeptember,April, JuneandNovember;all theresthave31exceptfor February,whichhas28days, or29daysinaleapyear.
Unitsoftime
• Timeismeasuredinunitssuchas hours (h), minutes (min), seconds (s), days, weeks, months and years
• Toconvertbetweenunitsoftime:
▷ 1h = 60min
▷ 1min = 60s ▷ 1day = 24h
1week = 7days
1year = 12months
• DMSconversion: MostscientificcalculatorshaveaDMS(degrees,minutesandseconds)button orfunctionthatconvertstimeinfractionordecimalformtohours,minutesandseconds.
e.g.2.26hours → 2◦15′36′′ meaning2hours,15minutesand36seconds.
• Elapsedtime istheamountoftimebetweenthestartandtheendofanactivityorevent.
• Use a.m. todescribethe12hoursbeforenoon,and p.m. todescribethe12hoursafternoon.
2 Whatunitoftimeismostappropriatetomeasureeachofthefollowing?
Lessonatschool a Reheatingamealinamicrowave b
Ageofaperson c Schoolholidays d
Accessingtheinternet e Movie f
3 UsetheDMSbutton/functiononyourcalculatortoconvertthefollowingtohoursandminutes, roundingtothenearestminutewherenecessary.
4 Whattimewillitbe: 4hoursafter5:30p.m.? a 7hoursbefore1:00p.m.? b 17hoursbeforemidday? c 15hoursafter2:00a.m.? d 3.5hoursafter1:00p.m.? e 2.25hoursbefore4:00a.m.? f
5 Thetimerequiredtobakeacakeinanovenis1h9min. Whenwillthecakebefinishedifthestartingtimeareas follows?
5:00a.m. a 9:00a.m. b 8:20p.m. c 10:34a.m. d
5:44p.m. e Midnight f 3:56p.m. g 10:51a.m. h
6 Addthesetimes.
2h24min + 2h14min a 4h04min + 1h46min b 5h30min + 3h30min c 7h41min + 5h50min d 11h29min + 6h55min e 9h09min + 3h59min f
7 Subtractthesetimes. 10h47min 2h22min a 4h52min 1h40min b 6h20min 5h08min c 8h10min 4h20min d 5h34min 2h18min e 10h46min 7h56min f
8 Findthedifferencebetweenthesetimes.
8:00p.m.and11:00p.m. a 2:15a.m.and9:25a.m. b 1:43p.m.and12:40p.m. c 11:05a.m.and9:35a.m. d 1:30p.m.andmidnight e 6:23a.m.and5:25p.m. f
9 Whatisthetime: 11hoursbefore2:00a.m.? a 5hoursafter7:00p.m.? b 1 1 2 hoursafter6:30a.m.? c 2 1 3 hoursbefore3:30p.m.? d 4hand11minafter1:45p.m.? e 12hand50minafter6:23a.m.? f
Laurenisacyclistwhorecordedthefollowingtrainingtimes atthegym.
1h21min59min
2h05min1h47min
45min1h35min
a Whatisthetotaltrainingtime?
b Whatisthemeantrainingtime?
c Whatisthemediantrainingtime?
Whatisthetime5hoursand29minutesafterthefollowingtimes?
Calculatethetime,indays,hoursandminutes,thathaselapsedbetweenthesetimes.
a 4:10a.m.Mondayand4:50p.m.Tuesdaythefollowingday
b 8:01a.m.Wednesdayand9:10a.m.thefollowingThursday
c 6:30p.m.Tuesdayand4:28a.m.thefollowingFriday
d 0700Saturdayand1300onthefollowingSunday
e 1020Tuesdayand1855onthefollowingFriday
f 0050Wednesdayand1915onthefollowingSaturday
16 Ivyleaveshomeat0928togoshopping.Shereturnsat1348.Howlong,inhoursandminutes,had shebeenaway?
17 Agameoffootballstartsat1412andfinishesat1559.Whatisthelengthofthegame?Answerin hoursandminutes.
18 Alexis’sdadisgoingtopickherupfromthecinemaoncethefilmhasfinished.Ifthefilmstartsat 1735andis99minuteslong,atwhattimewillheneedtopickherup?
19 Mason’sdogranawayfromhomeonMondayat3:15p.m.Thedogwasfoundthefollowing Thursdayat1300.Howmuchtimeelapsedbeforethedogwasfound?
7B LatitudeandLongitude
Learningintentions
• Touseandunderstandlatitudeandlongitude
• Toperformcalculationsandsolveproblemsinvolvinglatitudeandlongitude
Past,presentandfuturelearning
• Someoftheseconceptsmaybenewtostudents
• ThisisaYear11topicwhichisnotrepeatedorextendedinYear12
• QuestionsaboutlatitudeandlongituderegularlyappearinHSCExaminations
Earth’ssurfaceisdividedintoparallelsoflatitudeandmeridiansoflongitude,whichareimaginarylineson theEarth’ssurface,formingcirclesandagrid.Thisimaginarygridisusedtospecifythepositionofapoint ontheEarth’ssurface.Latitudeisananglenorthorsouthoftheequator,andlongitudeisanangleeastor westoftheGreenwichmeridian.TheangleoflatitudeistheangleattheEarth’scentrebetweentheplaneof theequatorandalinefromthecentretotheparalleloflatitude.Theangleoflongitudeislikewiseformed attheEarth’scentrebetweentheplaneoftheGreenwichmedianandalinefromthecentreoftheEarthto themeridianoflongitude.TheGreenwichorprimemeridianisanimaginarynorth–southlinethatpasses throughthetownofGreenwich(London).
Latitudeisgivenfirst(NorS)andthenthelongitude(EorW).Forexample,thepositionofSydneyis (33◦S,151◦E).Itis33◦ southoftheequatorand151◦ eastoftheGreenwichmeridian.
Example6
Describingpositionsofonepointrelativetoanotherpoint
DescribethepositionofCairo(30◦N,31◦E)relativetoSydney(34◦S,151◦E).
Solution
Explanation
Comparinglatitudes: Useasketchtohelpwithcomparing. Cairois64◦ northofSydney.
Comparinglongitudes: Cairois120◦ westofSydney.
Nowyoutry
DescribethepositionofRome(42◦N,12◦E)relativetoSydney(34◦S,151◦E).
Exercise7B
1 Example4 AdiagramofEarth’ssurfaceisshownbelow.Thecoordinatesof pointAare(60◦N,70◦E).
a WhatarethecoordinatesofpointB?
b WhatarethecoordinatesofpointC?
c Whatisthemaximumvaluepossibleforlatitude?Where doesitoccur?
2 Example5 Brusselsislocatedat(50◦N,4◦E).Limaislocatedat(12◦S,77◦W).
a Whichcityisclosertotheequator?
b WhatisthedifferenceinlatitudebetweenBrusselsandLima?
c WhatisthedifferenceinlongitudebetweenBrusselsandLima?
3 Tehranislocatedat(35◦N,51◦E).Wellingtonislocatedat(41◦S,174◦E).
a WhichcityisclosertotheGreenwichmeridian?
b WhatisthedifferenceinlatitudebetweenTehranandwellington?
c WhatisthedifferenceinlongitudebetweenTehranandWellington?
BUILDING
4
Nagoyaislocatedat(35◦N,136◦E).Determinethecoordinatesofapointthatis:
5
Belgradeislocatedat(44◦N,20◦E).Determinethecoordinatesofapointthatis:
6
Munichhasthecoordinates(48◦N,11◦E)andParishasthecoordinates(48◦N,2◦E)
a WhatdothesecitieshaveincommonintermsoftheirpositiononEarth’ssurface?
b Whatisthelongitudeofapoint20◦ duesouthofMunich?
c WhichcityisfurtherfromtheGreenwichmeridian?
d Whatarethecoordinatesofapoint80◦ dueeastofParis? DEVELOPING
7 Thefollowingtableshowsthelatitudeandlongitudeofcitiesaroundtheworld.
a Whichcityisclosesttothefollowinglatitudes?
Equator iii LatitudeofAthens
b Whichcityisclosesttothefollowinglongitudes?
c ListthecitiesintheNorthernHemisphere.
d ListthecitiesintheWesternHemisphere.
e Whichcitieshavethesamelatitude?
f Whichcitieshavethesamelongitude?
g WhichcityisclosesttotheNorthPole?
h WhichcityisclosesttotheSouthPole?
8
Describethefollowing:
a ThepositionoftheAthens(37◦N,23◦E)relativetoCairo(30◦N,31◦E).
b ThepositionoftheAdelaide(34◦S,139◦E)relativetoKualaLumpur(3◦N,101◦E).
c ThepositionoftheMontevideo(34◦S,56◦W)relativetoBirmingham(52◦N,1◦W).
d ThepositionoftheCairo(30◦N,31◦E)relativetoRiodeJaneiro(22◦S,43◦W).
CHALLENGING
9 Hobartislocatedat(42◦S,147◦E)andPortMoresbyislocatedat(9◦S,147◦E).
a DescribetherelativepositionsofthesecitiesonEarth’ssurface.
b Whatarethecoordinatesofapointhalf-waybetweenthesecities?
c Whatarethecoordinatesofapoint65◦dueeastofHobart?
d DescribethepositionofHobartrelativetoPortMoresby.
10 Kingstonislocatedat(17◦N,76◦W).Jakartaislocatedat(6◦S,106◦E).
a WhatisthedifferenceinlatitudebetweenKingstonandJakarta?
b WhatisthedifferenceinlongitudebetweenKingstonandJakarta?
c Whatarethecoordinatesofapoint20◦ duesouthofKingston?
d Whatarethecoordinatesofapoint80◦ dueeastofJakarta?
e DescribethepositionofJakartarelativetoKingston.
11 InthisdiagramoftheEarth, O representsthecentre,andHisa pointlocatedonboththeequatorandtheGreenwichmeridian.
a FindthecoordinateofthepointJ.
b Findthecoordinateofthepointthatis:
i 12◦ duenorthofpointJ
ii 45◦ duesouthofpointJ
iii 55◦ duewestofpointJ
iv 150◦ duewestofpointJ
v 102◦ dueeastofpointJ.
c DescribethepositionofpointJrelativetopointH.
d Torontohascoordinates(44◦N,80◦W).Describethepositionof TorontorelativetopointJonthediagram.
Communicateyourreasoning,understandingandfluency
12 TheGalapagosIslandsandSingaporearelocatedatthesamelatitude. ThelongitudeoftheGalapagosIslandsis92◦W.ThelongitudeofSingaporeis104◦E. YouneedtogetfromGalapagosIslandstoSingaporeasquicklyaspossible. Wouldyougoeastorwest?Explainwhy.
Timezones
• Linesoflongitudearegenerallyusedasthebasisoftimezones.
• TimeisbasedonthetimeinaplacecalledGreenwich,UnitedKingdomandthisiscalled CoordinatedUniversalTime(UTC)orGreenwichMeanTime(GMT).
• Australiahasthreetimezones:
▷ EasternStandardTime(EST),whichisUTCplus10hours.
▷ CentralStandardTime(CST),whichisUTCplus9.5hours.
▷ WesternStandardTime(WST),whichisUTCplus8hours.
UNCORRECTEDSAMPLEPAGES
• Daylightsavingisthepracticeofmovingclocksforward,usuallybyonehour.
• TheInternationalDateLineseparatesonecalendardayfromthenext,passingthroughthe mid-PacificOceanwithalongitudeof180◦ .
• Themaponthenextpageshowsthetimezonesallaroundtheworld.
Example7
Solvingproblemsusingatimezone
HobartislocatedintheAustralianEasternStandardTimezone(+10)andGreenwichisattheCoordinated UniversalTime(UTC)intimezone(0).Whatisthetimein:
a Hobartifitis8:00p.m.inGreenwich?
b Greenwichifitis5:30a.m.inHobart?
Solution Explanation
a Hobart = 8:00p.m. + 10hours = 6:00a.m.
b Greenwich = 5:30a.m. 10hours = 7:30p.m.
Nowyoutry
HobartisintheEST(+10)zoneandis10hours aheadofUTCatGreenwich.Addthetime.
GreenwichisatUTCandis10hoursbehind Hobart,whichisinEST(+10).Subtractthetime.
PerthislocatedintheAustralianWesternStandardTimezone(+8)andGreenwichisattheCoordinated UniversalTime(UTC)intimezone(0).Whatisthetimein:
a Perthifitis11:00a.m.inGreenwich?
b Greenwichifitis9:30a.m.inPerth?
11
12 Example8
NewcastleispartoftheEasternStandardTimezoneandis10hoursaheadofUTC.Whatisthe standardtimeinGreenwichwhenitis5:00p.m.FridayinNewcastle?
Findthetimeinthefollowingcitiesifitis11:30a.m.daylightsavingtimeinSydney(UTC+10).
Perth(UTC+8) a Brisbane(UTC+10) b Malta(UTC+1) c Suva(UTC+12) d Vancouver(UTC 8) e Belfast(UTC0) f
UNCORRECTEDSAMPLEPAGES
13
Sydneyis10hoursaheadofUTCandSeattleis8hoursbehindUTC.
a Whatisthetimedifferencebetweenthetwocities?
b WhatisthetimedifferenceifSydneyisondaylightsavingtimeandSeattleisonstandardtime?
14 WhatisthetimedifferencebetweenTasmaniaandSriLankaifTasmaniaisondaylightsavingtime andSriLankaisonstandardtime?Tasmaniais10hoursaheadofUTCandSriLankais5hours aheadofUTC.
15 PeopleinNewSouthWales(UTC+10)turntheirclocksforwardsonehourfordaylightsaving. WesternAustralia(UTC+8)doesnotadjustitsclocksfordaylightsaving.
a Insummer,whatisthetimeinNewSouthWalesifitis3:10p.m.inWesternAustralia?
b Insummer,whatisthetimeinWesternAustraliaifitis10:30a.m.inNewSouthWales?
16 DaylightsavingoperatesinthesummermonthsinVictoriaandNewSouthWales,butnotinthe NorthernTerritory,QueenslandnorWesternAustralia.
Melbourne(Vic),Sydney(NSW)andBrisbane(Qld)arepartoftheAustralianEasternStandard Time(UTC+10).
Darwin(NT)ispartoftheAustralianCentralStandardTime(UTC+9.5). Perth(WA)ispartofAustralianWesternStandardTime(UTC+8).
Observingdaylight savingtime:
a WhatisthetimeinSydneyifitis3:15p.m.inBrisbane?
b WhatisthetimeinDarwinifitis1:15a.m.inMelbourne?
c WhatisthetimeinPerthifitis6:20p.m.inBrisbane?
d Ifitis10:35a.m.inMelbourne,whatisthetimeinPerth?
17 AriadneisonaholidayinToronto(UTC 5).ShewantstostreamtheMatildas’semi-finalWorld CupmatchplayedinSydney(UTC+10)onFriday16Augustat8:00p.m. TorontoissubjecttodaylightsavingtimeinAugust,butSydneyisnot.
WhattimeanddayinTorontoshouldAriadnestartstreamingthematch?Usecalculationstosupport youranswer.
7D Timedifferenceusingtimezones
Learningintentions
• TouseandunderstandCoordinatedUniversalTime(UTC)
• TosolvepracticalproblemsusingCoordinatedUniversalTime(UTC) Past,presentandfuturelearning
• Someoftheseconceptsmaybenewtostudents
• ThisisaYear11topicwhichisnotrepeatedorextendedinYear12
• QuestionsabouttimezonesregularlyappearinHSCExaminations
Theinternationaltimezonescanbeusedtocalculatethelocaltimeintwolocations.First,findthetime differencebetweenthetwolocationsbysubtractingthetimezones.Thendrawaneast–westtimelineand placethelocationsonthetimeline.Tofindthelocaltimeyouneedtoaddorsubtractthetimedifference.If therequired timeiseastofthegiventimethenaddthetimedifference.Alternatively,iftherequiredtimeis westof thegiventimethensubtractthetimedifference.
Timedifferenceandlocaltime
Tocalculatethelocaltime:
1 Findthetimedifferencebetweenthetwolocations.
2 Placethelocationsonaneast–westtimeline.
3 Findthelocaltimebyaddingorsubtractingthetimedifference.
− West East +
• Eastoflocationwiththegiventime(movingwesttoeast).Addthetimedifference.
• Westoflocationwiththegiventime(movingeasttowest).Subtractthetimedifference.
Example9
Findingthetimedifferenceandlocaltime
PatrickisworkinginSeoul(UTC +9)andneedstotraveltoChicago(UTC 6).
a Whatisthetimedifferencebetweentheseplaces?
b WhatisthelocaltimeinChicagoifitis5:00p.m.inSeoul?
c AflightleavesSeoulat5:00p.m.andfliesnon-stoptoChicago.Theflighttakes14hours.Whatisthe timeinChicagowhentheflightarrives?
Solution
a Timedifference =+9 ( 6) = 15h
b
− West Chicago Seoul East +
UNCORRECTEDSAMPLEPAGES
TimeinChicago = 5:00p.m. 15h = 2:00a.m.
TimeinChicagois2:00a.m.
c TimeinChicago = 2:00a.m. + 14h = 4:00p.m.
TimeinChicagois4:00p.m
Explanation
Timedifferenceisdeterminedbythedifferencein longitude.AddthelongitudeofChicagotothatof Seoul.
Drawaneast–westtimeline. MarkChicago(UTC 6)ontheleft-handsideand Seoul(UTC +9)ontheright-handside.
RequirethetimeinChicago.Itiswestofthe locationwiththetimeinformation. Subtractthetimedifference.
Writetheanswerinwords.
Flighttakes14hours.Addthetimefortheflightto thelocaltimeofthedestination.
Writetheanswerinwords.
8
DEVELOPING
AplaneleavesMelbourne(UTC +10)andfliestoParis(UTC +1).Theflighttakes23hours.The planeleavesMelbourneat4:00p.m.Thursday.Onwhatdayandatwhattimedoestheplanearrive inParis?
9 NacallsafriendinBeijingfromLosAngeles.Beijingis8hoursaheadofUTCandLosAngelesis 8hoursbehindUTC.Itis8:15p.m.inLosAngelesandtheytalkfor30minutes.Whatisthetimein Beijingattheendofthephonecall?
10 Adelaide(UTC +9.5)islocatedintheCentral StandardTimezone.Melbourne(UTC +10) islocatedintheAustralianEasternStandard Timezone.
a WhatisthetimeinAdelaideifitis 5:45a.m.inMelbourne?
b WhatisthetimeinMelbourneifitis 2:10p.m.inAdelaide?
c Atwhattimewillatrainarrivein AdelaideifitdepartsMelbourneat 7:00a.m.andtraveltimeis10hours?
11 AndrewisplanningatripfromTownsville(UTC +9.5)toHongKong(UTC +8).
a WhatisthetimeanddayinHongKongifitis7:30a.m.on5JuneinTownsville?
b AflightleavesTownsvilleat7:30a.m.andfliesnon-stoptoHongKong.Theflightisintheairfor 7hours.WhattimeanddayisitinHongKongwhentheflightarrives?
12 AboatdepartsBrisbaneonTuesday12Octoberat12:00p.m.andtakes15 1 2 daystotravelwestto Honolulu.Brisbaneis10hoursaheadofUTCandHonoluluis10hoursbehindUTC.
a WhatisthelocaltimeanddayinHonoluluwhentheboatdepartsBrisbane?
b WhatisthelocaltimeanddaywhentheboatarrivesinHonolulu?
13 AplaneleavesSydneyat2:00a.m.Tuesday17Mayforan8hourflighttoKabul.Sydneyis 10hoursaheadofUTCandKabulis4hoursaheadofUTC.
a WhatisthelocaltimeanddaywhentheplanearrivesinKabul?
b ThereturnflightleavesKabulat2:00p.m.onthenextFriday.Whatisthetimeanddaywhenthe planearrivesinSydney?
14 TheUniversalCoordinatedTime(UTC)ofSamoais 11hours.Whenitis9:00p.m.Wednesdayin Samoa,itis3:00p.m.ThursdayinBangkok.WhatistheUTCofBangkok?
15 AplanetravelsfromParis(UTC +1)toSanFrancisco(UTC 8).TheflightfromParisto SanFranciscotakes11hours30minutes.IftheflightleavesParisonWednesdayat1420,whatday andtimewilltheflightarriveinSanFrancisco?
Example11
Findthetimedifferenceandlocaltime
Aucklandislocatedat(37◦S,175◦E)andWollongongislocatedat(34◦S,150◦E).
a Calculatethedifferenceinlongitudebetweenthesetwocities.
b Whatisthetimedifferencebetweenthesetwocities?
c WhatisthetimeinAucklandifitis2:00p.m.inWollongong?
d WhatisthetimeinWollongongifitis9:00a.m.inAuckland?
Solution
UNCORRECTEDSAMPLEPAGES
Explanation
a Longitudedifference = 175 150 = 25◦ Time differenceisdeterminedbythedifferencein longitude. Bothlocationsareontheeastside,sosubtract.
b Timedifference = 25◦ × 4min = 100min ÷ 60 = 1h40min
c Aucklandis2:00p.m. + 1h40min = 3:40p.m.
Itis3:40p.m.inAuckland.
d Wollongongis9:00a.m.–1h40min = 7:20a.m.
Itis7:20a.m.inWollongong.
Nowyoutry
Multiplythelongitudedifferenceby4minutesto findthetimedifference. 100minutes ÷ 60 = togethoursandminutes Usethe buttononthecalculatortoconvert 100minutestohoursandminutes.
Wollongong
Add time – West East +
AucklandiseastofWollongong. ADDthetimedifference.
Wollongong Auckland
150°E
Subtract time – West East + 175°E
WollongongiswestofAuckland. SUBTRACTthetimedifference.
Christchurchislocatedat(44◦S,173◦E)andSydneyislocatedat(34◦S,151◦E).
a Calculatethedifferenceinlongitudebetweenthesetwocities.
b Whatisthetimedifferencebetweenthesetwocities?
c WhatisthetimeinChristchurchifitis3:30p.m.inSydney?
d WhatisthetimeinSydneyifitis11:00a.m.inChristchurch?
Example12
Findthetimedifferenceandlocaltime
Chicagoislocatedat(42◦N,88◦W)andSeoulislocatedat(38◦N,127◦E).
a WhatisthelocaltimeinChicagoifitis5:00p.m.inSeoul?
b AflightleavesSeoulat5:00p.m.andflies14hoursnon-stoptoChicago. WhatisthelocaltimeinChicagowhentheflightarrives?
Solution
a Longitudedifference = 88 + 127 = 215◦
Time difference = 215◦ × 4minutes = 860minutes ÷ 60 = 14h20min
TimeinChicago = 5:00p.m. 14h20min = 2:40a.m.
Itis2:40a.m.inChicago
b TimeinChicago = 2:40a.m. + flighttime = 2:40a.m. + 14 hourflight = 4:40p.m.
Itis4:40p.m.whentheflightlandsinChicago.
Nowyoutry
Explanation
Timedifferenceisdeterminedbythedifferencein longitude. Onelocationiseast,theotherwest,soADD longitude.
Multiplythelongitudedifferenceby4minutesto findthetimedifference. 860minutes ÷ 60 = togethoursandminutes Usethe buttononthecalculatortoconvert 860minutestohoursandminutes.
Theflighttakes14hours. Addtheflighttimetothelocaltimeofthe destination.
NewYorkislocatedat(40◦N,74◦W)andSingaporeislocatedat(1◦N,104◦E).
a WhatisthelocaltimeinNewYorkifitis3:00p.m.inSingapore?
b AflightleavesSeoulat3:00p.m.andflies16hoursnon-stoptoNewYork.Whatisthelocaltimein NewYorkwhentheflightarrives?
Exercise7E
1 Whatisthetime:
BUILDING
11hoursbefore2:00a.m.? a 5hoursafter7:00p.m.? b 1hour30minutesafter6:30a.m.? c 2hours15minutesbefore3:30p.m.? d 4hoursand11minutesafter1:45p.m.? e 12hoursand50minutesafter6:23a.m.? f
2 Example11 UsetheDMSbutton/functiononyourcalculatortoconvertthefollowingtohoursandminutes. 100minutes a 176minutes b 344minutes c 605minutes d 231minutes e 792minutes f
3 Calculatethedifferenceinlongitudebetweenthefollowingpoints. (72◦S,54◦E)and(16◦S,14◦E) a (25◦N,55◦E)and(35◦N,104◦E) b (40◦N,75◦W)and(49◦N,123◦W) c (15◦S,5◦W)and(80◦N,68◦W) d (25◦N,30◦W)and(42◦S,10◦E) e (61◦S,29◦E)and(28◦N,7◦W) f
10
11
12
CHALLENGING
JulialivesinSydney(34◦N,151◦E)andherbrotherTylerlivesinLosAngeles(34◦N,120◦E).
a WhatisthetimedifferencebetweenSydneyandLosAngeles?
b JuliawouldliketotelephoneTyleratmidnightonSundayforNewYearsEve. AtwhattimeandwhatdayinSydneyshouldJuliacall?
NewYorkhascoordinates(40◦N,75◦W)andthecoordinatesforNaplesare(40◦N,14◦E).
a WhatisthetimedifferencebetweenNewYorkandNaples?
b Itis10:30p.m.onFridayinNaples.WhatisthetimeanddayinNewYork?
PatricklivesinMelbourne(38◦S,145◦E).HewantstowatchafootballgamebeingplayedinBrazil (13◦S,50◦W)startingat7:00p.m.onSaturday.WhatisthetimeanddayinMelbournewhenthe gamestarts?
13 Example12 Singaporeislocatedat (1◦N,105◦E) andCanberraislocatedat(35◦S,149◦E).
a Showthatthereisa3-hourtimedifferencebetweenthetwocities.
b HarrylivesinCanberraandwantstoringafriendinSingapore.Whatisthetimeanddayin Singaporeifitis11:00p.m.FridayinCanberra?
c Harry’sfriendinSingaporesenthimaparcelwhichtakes7hoursofflighttimetoreachhim.It wassentat9:00a.m.Friday,Singaporetime.WhatwasthetimeanddayinCanberrawhenHarry receivedtheparcel?
14 TheGoldCoastislocatedat(28◦S,153◦E)andBaliislocatedat(8◦S,116◦E).
a WhatisthetimeinBaliifitis9:00a.m.intheGoldCoast?
b AflightleavestheGoldCoastat11:00a.m.andfliesnon-stoptoBali.Theflightisintheairfor 6hours.AtwhattimedoestheflightarriveinBali?
15 ThestandardtimeinDubboisbasedonthe149◦EmeridianandthestandardtimeinFremantleis basedonthe116◦Emeridian.
a IsabellaisinDubboandringsafriendinFremantleat8:00p.m.onaSaturday.Whatdayand timeisitinFremantle?
b Isabellacaughtaplaneat8:00p.m.onaSaturdayfromDubbotoFremantle.Thetraveltimefor thetripwas7hoursand30minutes.WhatisthetimewhenIsabellaarrivesinFremantle?
16 MollyflewfromSydney(34◦N,151◦E)toChittagong(22◦N,91◦E).HerplaneleftSydneyat 8:30a.m.Thursday(Sydneytime),stoppedfor4hoursinSingaporeandarrivedinChittagongat 1:00p.m.Thursday(Chittagongtime).Whatwasthetotalflyingtime?
17 LucyissailingacrossthePacificOceanfromapositionof(0◦,130◦W)toTahitiat(18◦S,150◦W). At8:30a.m.onSaturday9July,shecallshersisterinTahiti.WhatisthelocaltimeanddateinTahiti whenhersisterreceivesthecall?
18 Usingtheinternet,canyoufindaflightthatleavesandarrivesatthesametimeandthesameday?Is theplaneflyingeastorwest?
7C 11
7C 12
IcanfindthelocaltimebetweenlocationsusingCoordinatedUniversalTime(UTC).
e.g.Ifitis4:00p.m.inSydney(UTC +10),whatisthelocaltimeinNewYork(UTC 7)?
IcanfindthelocaltimebetweenlocationsusingCoordinatedUniversalTime(UTC)and daylightsavingtime.
e.g.Ifitis11:30a.m.daylightsavingtimeinSydney(UTC +10),whatisthelocaltimeinSuva, Fiji(UTC+12)?
7D 13
IcansolvepracticalproblemsusingCoordinatedUniversalTime.
e.g.AplaneleavesMelbourne(UTC +10)andfliestoParis(UTC +1).Theflighttakes 23hours.TheplaneleavesMelbourneat4:00p.m.onThursday.Onwhatdayandtime doestheplanearriveinParis?
7E 14 Icancalculatethedifferenceinlongitudebetweentwolocations.
e.g.CalculatethedifferenceinlongitudebetweenAuckland(37◦S,175◦E)andWollongong (34◦S,150◦E).
7E 15 Icanfindthetimedifferenceusing 1◦ = 4 minutes.
e.g.CalculatethetimedifferencebetweenAuckland(37◦S,175◦E)andWollongong (34◦S,150◦E).
7E 16 Icanfindthelocaltimebetweenlocationsusinglongitude.
e.g.WhatisthetimeinAuckland(37◦S,175◦E)ifitis2:00p.m.inWollongong(34◦S,150◦E)?
7E 17 Icansolvepracticalproblemsusinglongitude.
e.g.AflightleavesSeoul(1◦N,104◦E)at3:00p.m.andflies16hoursnon-stopto NewYork(40◦N,74◦W).WhatisthelocaltimeinNewYorkwhentheflightarrives?
Multiple-choicequestions
1 7A Theschoolbustakes49minutestogetfromJoseph’shousetotheschool.Ifschoolstartsat8:30 a.m.,whatisthelatesttimeJosephcancatchthebustogettoschoolontime?
2 7A Atrainleavesthestationat7:28a.m.Thejourneytoitsfinaldestinationtakes6hoursand54 minutes.Whatisthetrain’sarrivaltime?
3 7B CityAisatlatitude26◦Sandlongitude133◦E.CityBis35◦ northofCityAand21◦ westofCityA. WhatarethelatitudeandlongitudeofCityB?
4 7B ThecoordinatesofDublinare(53◦N,6◦W).WhatarethecoordinatesofHamburgifitis16◦ east ofDublin? (53◦N,10◦E) A (53◦N,22◦W) B (69◦N,6◦W) C
5 7C WhatisthetimedifferencebetweenSingapore(UTC +8)andCanberra(UTC +10)?
6 7C WhatisthetimeinStJohn’s(UTC 3.5)ifitis4.00a.m.inDallas(UTC 6)?
7 7C ThetimeinGreenwichontheprimemeridianis3:00p.m.Whatisthestandardtimein KualaLumpur(UTC +8)?
8 7C
Whenitis4:30p.m.daylightsavingtimeinAdelaide(UTC +9.5),thelocaltimeinBrisbane (UTC +10),whichdoesnothavedaylightsavingtime,is: 5:00p.m. A 4:00p.m.
9 7D Perth,inWesternAustralia,is8hoursaheadofGreenwich,inEngland.Athens,inGreece,is2hours aheadofGreenwich.
WhatisthetimeinAthenswhenitis1:00p.m.inPerth? 3:00a.m. A 7:00a.m. B 7:00p.m. C 11:00p.m. D
10 7E Thedifferenceinlocaltimebetween(43◦N,100◦W)and(17◦S,15◦W)is 7h40min A 5h40min B 4h C 1h44min D
11 7E WhenitisnooninGreenwich,thelocaltimeinVancouver(49◦N,123◦W)is 8:12p.m. A 8:20a.m. B 3:48p.m. C 3:48a.m. D
UNCORRECTEDSAMPLEPAGES
Short-responsequestions
1 7A Completethefollowing.
= s a
= h d
= days g
= h b
= min e
= h h
2 7A Whatisthetime7hoursand10minutesafterthefollowingtimes? 0800 a 1325 b
= min c
= days f
= min i
3 7A Luke’sfootballteamstartsitsgameat10:15a.m.Theteamplaystwohalvesthatare25minuteseach andthereisa6-minutebreakathalftime.
a Lukescoresagoal5minutesafterhalftime.Atwhattimedoeshescorehisgoal?
b Atwhattimedoesthegamefinish?
4 7B Karachiislocatedat(25◦N,67◦E)andSalvadorislocatedat(13◦S,39◦W).
a WhichcityisclosertotheGreenwichmeridian?
b WhatisthedifferenceinlatitudebetweenKarachiandSalvador?
c Whatis thedifferenceinlongitudebetweenKarachiandSalvador?
5 7B Monterreyislocatedat(26◦N,100◦W)andAucklandislocatedat(37◦S,174◦E).
a WhatisthedifferenceinlatitudebetweenMonterreyandAuckland?
b Whatis thedifferenceinlongitudebetweenMonterreyandAuckland?
c Whatare thecoordinatesofapoint50◦ duesouthofMonterrey?
d Whatarethecoordinatesofapoint50◦ duewestofAuckland?
6 7C WhatisthetimeinBoston(UTC 5)whenitis1:00p.m.inHanoi(UTC +7)?
7 7C Perth(UTC +8)islocatedintheWesternStandardTimezone.Brisbane(UTC +10)islocatedinthe EasternStandardTimezone.
a WhatisthetimedifferenceinhoursbetweenPerthandBrisbane?
b Whatis thetimeinPerthifitis5:00p.m.inBrisbane?
8 7D AflightfromSydney(UTC +10)toAdelaide(UTC +9.5)takestwohoursflyingtime.
a WhatisthetimedifferenceinminutesbetweenSydneyandAdelaide?
b Aplane leavesSydneyat7:00a.m.AtwhattimewillitarriveinAdelaide,takingintoaccountthe flyingtime?
9 7D TheGoldCoast’stimezoneisUTC +10andBali’stimezoneisUTC +8.
a WhatisthetimeinBaliifthetimeintheGoldCoastis9:00a.m.?
b AflightleavestheGoldCoastat11:00a.m.andfliesnon-stoptoBali.Theflightisintheairfor 3hours.AtwhattimedoestheflightarriveinBali?
10 7E Whenitis1:30p.m.inNewYork(40◦N,75◦W),whatisthelocaltimeinSeattle(47◦N,123◦W)?