小学五年级奥数试题行程问题(北大奥数卷)（primary school grade five olympiad questions travel problems (peking university mathematical olympiad volume)）

小学五年级奥数试题行程问题北大奥数卷（PRIMARYSCHOOLGRADEFIVEOLYMPIADQUESTIONSTRAVELPROBLEMSPEKINGUNIVERSITYMATHEMATICALOLYMPIADVOLUME）PRIMARYSCHOOLGRADEFIVEOLYMPIADQUESTIONSTRAVELPROBLEMSPEKINGUNIVERSITYMATHEMATICALOLYMPIADVOLUMEINPEOPLESLIVES,THEREARETHREEIMPORTANTTHINGS,“DISTANCE“,“SPEED“AND“TIME“THETYPICALAPPLICATIONOFTHESETHREEQUANTITIESISCALLEDTHESTROKEPROBLEMTHERELATIONBETWEENTHESETHREEQUANTITIESCANBEREPRESENTEDBYTHEFOLLOWINGFORMULADISTANCESPEEDTIMESPEEDDISTANCE/TIMETIMEDISTANCE/SPEEDTHEENCOUNTERPROBLEMANDTHERETRIEVALPROBLEMARETWOIMPORTANTTYPESOFTHETRAVELPROBLEMTHEPROBLEMOFMEETINGISWHENTWOOBJECTSTRAVELINOPPOSITEDIRECTIONS,ANDTHENTHEYMEETATACERTAINPOINTONTHEWAYTHEMAINQUANTITATIVERELATIONISTOTALDISTANCESPEEDANDMEETINGTIMETHEPROBLEMOFCHASINGISWHENTWOOBJECTSTRAVELINTHESAMEDIRECTION,ANDTHEWALKERFOLLOWSTHESLOWWALKERSJOURNEYTHEMAINQUANTITATIVERELATIONISDISTANCEDIFFERENCESPEEDDIFFERENCETRACKINGTIMEEXAMPLE1SISTERCOMEHOMEFROMSCHOOL,AT80METERSPERMINUTEWALKHOME,12MINUTESLATER,SISTERRIDINGATTHESPEEDOF240METERSPERMINUTEFROMSCHOOLTORIDEHOME,AFTERAFEWMINUTES,SISTERCANCATCHUPWITHMYSISTERANALYSISAFTER12MINUTES,MYSISTERARRIVEDATA,ANDMYSISTERRODEHOMEASSHOWNINTHEFOLLOWINGFIGUREASCANBESEENFROMTHEPICTURE,SISTERFROMTHESTARTTOCATCHUPWITHHERSISTERTHISPERIODOFTIME,SISTERTHANSISTERLINETRIPISTHESISTER12MINUTESWALK,THATIS,SISTERANDSISTERSROADDIFFERENCEIFTHEREISADISTANCEDIFFERENCE,THENWECANFINDOUTTHESPEEDDIFFERENCE,ACCORDINGTOTHEQUANTITYRELATIONBETWEENTHECHASEANDTHEPROBLEMCHASEANDTIMEDISTANCEDIFFERENCE,SPEEDDIFFERENCEICANFINDMYSISTERSTIMETOCATCHUPWITHMYSISTERANSWERSISTERANDSISTERSROADDIFFERENCE80X12960KMTHESPEEDDIFFERENCEBETWEENMYSISTERANDMYSISTER24080160KMTIMEFORMYSISTERTOCATCHUPWITHMYSISTER960/1606POINTSANSWERAFTER6MINUTES,MYSISTERCAUGHTUPWITHHERSISTEREXAMPLE2ABUSANDACARRUNATTHESAMETIMEFROM360KILOMETERSAPARTTHEBUSRUNS35KILOMETERSPERHOURTHECARRUNS55KILOMETERSPERHOURAFTERAFEWHOURS,THETWOCARSARE90KILOMETERSAPARTANALYSISTWOCARSFROM360KILOMETERSAWAYFROMTHE90ATTHESAMETIME,THEOPPOSITEDIRECTION,THEDISTANCEGRADUALLYSHORTENED,ATSOMEPOINTBEFORETHEENCOUNTER,TWOCARSARESEPARATEDBYTWOKILOMETERSFOLLOWINGCHARTATTHISTIME,THETWOVEHICLESARETRAVELINGTOGETHERFORTHEJOURNEY36090270KMITISWORTHNOTINGTHAT,WHENTHETWOCARSMETTOCONTINUEDRIVING,THEDISTANCEBETWEENTHETWOVEHICLESGRADUALLYINCREASEDFROMZERO,ANDATSOMEPOINT,THETWOCARSARE90KILOMETERSAPARTASSHOWNINTHEFOLLOWINGFIGUREASYOUCANSEEFROMTHEDIAGRAM,ATTHISTIME,THETWOCARSARETRAVELINGTOGETHER36090450KMACCORDINGTOTHEQUANTITYRELATIONOFTHEENCOUNTERPROBLEMMEETTIMEDISTANCE/SPEEDANDTHEQUESTIONYOUASKCANBEANSWEREDANSWERBEFOREMEETING36090830193555270/903TIMEAFTERMEETING360903555450/905TIMEANSWERTWOCARSAFTERDEPARTURE3HOURSAPART90KILOMETERS,5HOURSAFTERDEPARTURE90KILOMETERSAPARTAGAINEXPLANATIONTHETWOCARSHAVENOTMETEACHOTHERONTHESURFACE,THOUGHITISNOTTHEPROBLEMOFMEETINGEACHOTHER,THETWOCARSALLHAVETHESAMETIME,SOTHEYCANBEANSWEREDASAMEETINGPROBLEM3BROTHERSANDTWOPEOPLERODEBICYCLESHOMEFROMSCHOOLATTHESAMETIMEMYBROTHERRUNS15KILOMETERSPERHOUR,ANDHISBROTHERTRAVELS10KILOMETERSPERHOURAFTERHALFANHOURSDEPARTURE,MYBROTHERRETURNEDTOSCHOOLFOR1HOURS,ANDTHENLEFTFORHISYOUNGERBROTHERWHENMYBROTHEROVERTOOKMYBROTHER,HOWMANYKILOMETERSAWAYWASTHESCHOOLANALYSISTHESUBJECTCANBECONSIDEREDSEPARATELY,FROMTHEBEGINNINGSTEPBYSTEPANALYSISHALFANHOURLATER,MYBROTHERRETURNEDTOSCHOOLBECAUSEOFTHEINCIDENTINTHEPROCESS,MYBROTHERANDBROTHERSTAYEDINTHESCHOOLFOR1HOURSWHENIGOTTOSCHOOL,MYBROTHERWASDETAINEDFORANOTHER1HOURSTHENMYBROTHERTOOKANOTHER1HOURSTHEREFORE,ITCANBESEENTHATWHENHISBROTHERWASGOINGTOPURSUEHISBROTHERFROMSCHOOL,HISBROTHERSPENT2HOURS,ANDHISBROTHERS2HOURJOURNEYWASTHEDIFFERENCEBETWEENHISBROTHERANDHISBROTHERANSWERBROTHERFROMSCHOOLBEGANTOCHASEHISBROTHERSROADDIFFERENCE10X05X2120KMMYBROTHERSCATCHINGUPWITHHISBROTHER208301915104TIMETHEDISTANCETHEBROTHERWASLEAVINGWHENHEOVERTOOKHISYOUNGERBROTHER15X460KMAMYBROTHERWAS60KILOMETERSFROMSCHOOLWHENHECAUGHTUPWITHHISBROTHERZHANGXIAOMING,4CASESOFTWOPEOPLEATTHESAMETIMESTARTINGFROMTHEOPPOSITELINEBETWEENAANDB,TWOPEOPLEINTHEFIRSTMEETINGPLACEFROM40METERS,METTWOPEOPLESTILLUSETHEORIGINALSPEEDTOCONTINUEDRIVING,ANDINTHEIRRESPECTIVEREACHEACHOTHERSTARTINGPOINTIMMEDIATELYAFTERTHERETURNALONGTHESAMEROUTE,ONTHEWAYTHETWOMEETATADISTANCEOF15METERSBSECONDTIMESHOWMANYMETERSARETHEDISTANCESBETWEENAANDBANALYSISACCORDINGTOTHEPROBLEMOFDRAWINGASFOLLOWSASCANBESEENFROMTHEPICTURE,WHENXIAOZHANGANDXIAOMINGMETFORTHEFIRSTTIME,THEDISTANCEBETWEENTHETWOLINESWASADISTANCEBETWEENAANDBATTHISTIME,XIAOZHANGMADE40METERSWHENTHEYMETFORTHESECONDTIME,XIAOZHANGWENTTHROUGHADISTANCEOFMORETHAN15METERSXIAOMINGWENTTHROUGHTWO,ANDTHEDISTANCEBETWEENTHEMWAS15METERS,ANDTHETWOPEOPLEHAD3TIMESTHEDISTANCEBETWEENAANDBTHEREFORE,XIAOZHANGFROMTHESTARTTOTHESECONDMEETING,THEJOURNEYSHOULDBEHISDEPARTUREFROMTHEFIRSTMEETINGOFTHETRIPTO3TIMES,YOUCANFINDOUTFROMHISDEPARTURETOTHESECONDMEETINGOFTHEJOURNEYKNOWTHEDISTANCE,THEDISTANCEBETWEENBBIJIAMORETHAN15METERS,THEDISTANCEBETWEENAANDBCANBEOBTAINEDANSWERXIAOZHANGFROMTHESTARTTOTHESECONDMEETINGOFTHETRIP40X3120MDISTANCEBETWEENAANDB12015105MANSWERAANDBARE105METERSAPARTBOTHENDSOFADIAMETERCIRCULARRUNWAY5CASESINACIRCUMFERENCEOF400METERS,AANDBTWORESPECTIVELYATASPEEDOF6METERSPERSECONDAND4METERSPERSECONDBYBIKEATTHESAMETIMETOSTARTCLOCKWISEALONGTHECIRCUMFERENTIALROAD,AFTERALONGTIME,THETWOTIMEJIADICATCHUPWITHBANALYSISASTHECHART,ATTHETIMEOFDEPARTURE,AANDBTWOISHALFTHECIRCUMFERENCE,ACCORDINGTOTHEDISTANCEDIFFERENCE,SPEEDDIFFERENCECHASEANDTIME,WECANFINDATIMEAFTERTIMEBWHENANAILHITSTHESECOND,THETWOCANSEETHESAMEPLACEANDGOTHESAMEWAYTOCATCHAB,THANBRIDEACIRCLEOF400METERS,CANBEOBTAINEDINTWOAFTERSECONDTIMEANSWERABACATCHTIME400/28301964100SECONDSATWOTIMEAFTERTIMEB40064200SECONDSTHETOTALAMOUNTOFTIMETAKEN100200300SECONDSANSWERAFTER300SECONDSAFTERATWOCATCHUPWITHBEXPLANATIONWHENTRAVELINGONANANNULARRUNWAY,THETWOCARSAREMOVINGINTHESAMEDIRECTIONATTHESAMETIMEIFYOUMEETAGAIN,THEWALKERMUSTTRAVELMORESLOWLYTHANTHESLOWRUNNER,IE,THEDISTANCEISTHEPERIMETEROFTHERINGTRACKEXAMPLE6BUSES,VANS,TRUCKS,THREECARS,BUSES60KILOMETERSPERHOUR,TRUCKSPERHOUR50KILOMETERS,TRUCKS55KILOMETERSPERHOURBUSESANDLORRIESFROMTHEEASTTOWN,TRUCKSFROMWESTTOWNATTHESAMETIME,THETRUCKMETTHEBUS,10HOURSLATERMETTHETRUCKHOWMANYKILOMETERSARETHETWOTOWNSAPARTFROMEACHOTHERANALYSISACCORDINGTOTHEDRAWINGWHENABUSANDATRUCKATTHEAMEETING,ANDTHEGOODSREACHINGTOB,AFTER10HOURS,THETRUCKCAMEWITHIN10HOURSINTHATTRUCK,TRUCKANDVANBANKISTHEDISTANCETHETRUCKANDBUSMEETBUSANDTRUCKFORDISTANCEDIFFERENCETHETIMEDIFFERENCEBETWEENAPASSENGERCARANDAFREIGHTCARISABTHETIMETAKENISTHEMEETINGTIMEBETWEENTHETRUCKANDTHEBUSANSWERDISTANCEBETWEENABCOACHANDTRUCKDISTANCE5550101050KMTIMEBETWEENPASSENGERCARANDTRUCK1050830196050105TIMEDISTANCEBETWEENTWOTOWNS605510512075KMANSWERTWOTOWNSARE12075KILOMETERSAPARTEXPLANATIONTHISISANAPPLICATIONQUESTIONWHICHCOMBINESTHEQUESTIONOFMEETINGANDTHEPURSUITOFPROBLEMTHEDIFFERENCEBETWEENAPASSENGERCARANDAFREIGHTCARIS1050KILOMETERSTHETIMETAKENISTHEMEETINGTIMEBETWEENTHETRUCKANDTHEPASSENGERTRAIN,WHICHISTHEKEYTOSOLVINGTHEPROBLEMREADINGMATERIALSHIPMEETSSTURMISAFRENCHMATHEMATICIAN,INMANYAREASOFMATHEMATICSHAVEMADEPIONEERINGWORKONETIME,STURMTOATTENDANINTERNATIONALCONFERENCE,AFRIENDTOASKHIMAQUESTIONEVERYDAYATNOON,ASHIPFROMHARVARDTONEWYORK,ANDEVERYDAYINTHESAMETIMEASHIPFROMNEWYORKTOHARVARD,THESHIPTOSAILFORSEVENDAYSANDNIGHTS,ONTHEWAYTOASK,EACHSHIPOUTFROMHARVARDAFTERBEFOREARRIVINGINNEWYORKTOMEETSEVERALSHIPSFROMNEWYORKTHESHIPCANYOUTRYTOGIVEASOLUTIONEXERCISES1AB,THETWOCITIES450KMAPART,AANDBTWOCARSFROMTHEACITYTOTHECITYOFB,ALINEOFCARS52KMPERHOUR,BLINEOFCARS38KMPERHOUR,THECARARRIVEDATTHECITYOFB,ARETURNIMMEDIATELYAFTERATOTALOFTWOVEHICLESTOTHENUMBEROFHOURSFROMDEPARTURETOMEETANALYSISACCORDINGTOTHEPROBLEMOFDRAWINGASFOLLOWSASYOUCANSEEFROMTHEDIAGRAM,THEDISTANCEBETWEENTHETWOCARSFROMTHESTARTTOTHEMEETINGISEXACTLYTHEDISTANCEBETWEENTHETWOAANDBCITIES,SOTHETIMEOFTHETWOCARSFROMTHEDEPARTURETOTHEMEETINGISEQUIVALENTTOTHETIMEREQUIREDBYTHE450VEHICLESFORTWOKILOMETERSOFTWOKILOMETERSANSWER450X2/5238900/9010TIMEANSWERTWOCARSFROMSTARTTOMEET,TAKE10HOURS2BROTHERTOWALKATHOME50METERSPERMINUTEFROMSCHOOL,12MINUTESLATER,HISBROTHERCAMEOUTFROMSCHOOLTORIDEHISBROTHER,THERESULTWAS800METERSAWAYFROMTHESCHOOLTOCATCHUPWITHHISBROTHERASKINGTHEYOUNGERBROTHERTORIDETHEBICYCLESPEEDANALYSISACCORDINGTOTHEPROBLEMOFDRAWINGASFOLLOWSWHENTHEYOUNGERBROTHEROVERTOOKHISBROTHER,HEWAS800METERSFROMTHESCHOOLTHE800METERSWERETHETWOTRIPBYTHEELDERBROTHER,ONEFOR12MINUTES,ANDTHEOTHERFORTHEYOUNGERBROTHERFROMHISDEPARTURETOHISBROTHERSTIMEANSWERBROTHERSTIMETOCATCHUPWITHHISBROTHER8001250/50800600/50200/504POINTSYOUNGERBROTHERSSPEED800/4200MANSWERMYBROTHERRIDES200METERSPERMINUTE3,EASTANDWESTTWOTOWNSARE100KILOMETERSAPART,A,B,TWOCARSFROMTHETWOTOWNSATTHESAMETIMESETOUTTOMEETEACHOTHER,MEETAFTER4HOURSITISKNOWNTHATAISFASTERTHANB3KMPERHOUR,ANDWHATISTHESPEEDOFAANDBTWOCARSANALYSIS100KMISTHETOTALDISTANCETRAVELEDBYTWOVEHICLES,4HOURSFORMEETINGTIMEACCORDINGTOTHEQUANTITYRELATIONOFTHEENCOUNTER,WECANFINDTHESPEEDOFTHETWOCARALSOKNOWNASTHESPEEDDIFFERENCEBETWEENTWOCARS,ACCORDINGTOTHEDIFFERENCEANDTHEPROBLEM,THESPEEDOFTHETWOCARSWILLBESOLVEDANSWERTWOCARSPEEDAND100/425KMARMORVELOCITY253,214KMBSPEED251411KMANSWERASPEEDOF14KILOMETERSPERHOUR,ANDTHESPEEDOFBIS11KILOMETERSPERHOUR4AFREIGHTCARTRAVELSATASPEEDOF65KILOMETERSPERHOURAPASSENGERTRAINTRAVELS1500KILOMETERSPERHOURAT80METERSBEHINDITHOWMANYMETERSISTHEDISTANCEBETWEENTWOCARSINTHE2MINUTESBEFORETHEBUSPASSESOVERTHEVANANALYSISWHENAPASSENGERCARPASSESOVERATRUCK,APASSENGERCARISCAUGHTUPINATRUCK,THEDISTANCEBETWEENTHETWOCARSISEQUAL2MINUTESBEFORETHEBUSPASSESOVERTHEVAN,THEDISTANCEBETWEENTHETWOCARSISTHEDIFFERENCEBETWEENTHECOACHANDTHECOACHWITHIN2MINUTESANSWER1HOURSDIFFERENCEBETWEENCOACHANDTRUCK806515KMTHEBUSIS2MINUTESSHORTOFTHETRUCK15X1000/60X2500MATHEBUSIS500METERSTWOMETERSAWAYFROMTHE2MINUTESBEFOREITPASSESTHEVANNOTEAFTERTHEQUESTIONBACKTOTHINKAGAIN,FOUNDTHEBACKOFTHETRUCKINTHEBUSCONDITIONOF1500METERSISREDUNDANT,NOMATTERHOWFARAPARTTOTWOCARS,PASSENGERCARSINMORETHAN2MINUTESBEFORETHETRUCK,TWOCARSFROMTHEDISTANCEISCONSTANTWESHOULDALSOPAYATTENTIONTOTHEINTERACTIONOFUNITS5,A,B,TWOPEOPLERIDINGATTHESAMETIMEFROMTHENORTHANDSOUTHSIDESOFTHEOPPOSITEDIRECTION,ALINEOF23KILOMETERSPERHOUR,B18KILOMETERSPERHOUR,TWOPEOPLEATTHEMIDPOINTOFTHE10KMFROMTHETWOMET,HOWMANYKILOMETERSNORTHANDSOUTHARETWOPLACESANALYSISACCORDINGTOTHEPROBLEMOFDRAWINGASFOLLOWSITCANBESEENFROMTHEFIGURE,AWALKFORMORETHANHALFOFTHENORTHSOUTHDISTANCEOF10KM,BHALFWAYNORTHSOUTHDISTANCEOF10KILOMETERSLESSFROMSTARTTOMEET,AMORETHANBWALKEDTWO10KILOMETERSALSOKNOWNAPERHOURMORETHANBLINE23185KMHOWMANYHOURSLATERWOULDAPERSONBE20KILOMETERSMORETHANBTHISTIMEISTHETIMEOFTHEENCOUNTER,ANDWITHTHEMEETINGTIME,THEDISTANCEBETWEENTHENORTHANDSOUTHCANBEFOUNDANSWERENCOUNTERTIME10X2/231820/54TIMENORTHANDSOUTH23184414164KMANSWERTHESOUTHANDTHENORTHARE164KILOMETERSAPARTEXPLANATIONTHESURFACEPHENOMENONOFTHESUBJECTISAMEETING,INESSENCE,ITHASTHECHARACTERISTICSOFCHASINGTHEREFORE,QUESTIONSCANBEANSWEREDANDANSWEREDINTHEPROCESSOFDOINGTHIS,WESHOULDGRASPTHENATUREOFTHESUBJECT,CONSIDERTHESPEEDANDTHESPEED,ANDCONSIDERTHECONDITIONSCAREFULLYDONOT“TWOPEOPLEFACETOFACE“IS“MEET“,“TWOPEOPLEBEFOREANDAFTER“IS“CHASING“AND“6REDANDBLUERUNNING,IFREDLETBLUERUN20METERS,WHILETHEREDRUN5SECONDSTOCATCHUPIFTHEREDLETBLUERAN4SECONDS,6SECONDSAFTERTHERED,BLUE,REDANDBLUEISTHENUMBEROFSPEEDANALYSISLETTHEREDBLUERUN20METERS,20METERSAWAYISTHERED,BLUE,REDRUN5SECONDSAFTER5SECONDSISBLUE,CHASEANDTIME,THUSWECANCALCULATETHEVELOCITYDIFFERENCEBETWEENTHEMIFTHEREDLETBLUERAN4SECONDS,6SECONDSAFTERTHEREDISBLUE,INTHISPROCESS,6SECONDSFORTHECHASEANDTHETIMEONTHEBASISOFTHEPREVIOUSCONDITION,THESPEEDDIFFERENCEANDTHERETRIEVALTIMECANBEUSEDTOFINDTHEDISTANCEDIFFERENCEINTHEPROCESSTHISDIFFERENCEIS4SECONDSFORTHEBLUEDISTANCE,SOTHESPEEDCANBEOBTAINEDANSWERTHESPEEDDIFFERENCEBETWEENTHETWO20/54MBLUESPEED6X4/46MLITTLEREDSPEED6410MANSWERREDRUN10METERSPERSECOND,RUN6METERSPERSECOND7,A,TWOSTOPS360KILOMETERSAPART,BUSANDTRUCKFROMSTATIONTOSTATIONATTHESAMETIMETHEBUSRUNS60KILOMETERSPERHOUR,THEFREIGHTTRAINRUNS40KILOMETERSPERHOUR,THEBUSSTOPSATTHESECONDSTOPFORHALFANHOUR,ANDTHENRETURNSTOTHESTATIONATTHEORIGINALSPEEDHOWMANYKILOMETERSDOESTHETWOCARMEETFROMTHESECONDSTATIONANALYSISASTHEBUSSTOPSATSTATIONBTHEVANSTILLRUNS,THEREFORE,ITCANBECONSIDEREDSEPARATELYANSWERTHEBUSARRIVEDATANOTHERTIME360/606TIMEWHENTHEPASSENGERCARRETURNS,THEFREIGHTCARHASTRAVELED40X605260KMWHENTHETRUCKFROMB360260100KMTHETIMETHEBUSRETURNEDTOMEETTHEVAN100/40601TIMETHEDISTANCEFROMTHEMEETINGPOINTB60X160KMANSWERBMEETTIMEDISTANCE60KM8,A,B,TWOPEOPLEFROMTHEEASTANDWESTATTHESAMETIME,RESPECTIVELY,IFTWOPEOPLEGOTHESAMEWAY,A28MINUTESTOCATCHUPWITHBIFTWOPEOPLEGOONTHEOPPOSITESIDE,8MINUTESMEETKNOWNBIS50METERSPERMINUTE,HOWMANYMETERSISTHEDISTANCEBETWEENTHEEASTANDTHEWESTANALYSISACCORDINGTOTHEPROBLEMOFDRAWINGASFOLLOWSASCANBESEENFROMTHEPICTURE,A28820POINTSWITHINTHEDISTANCETRAVELEDWITHB28836POINTSTHEDISTANCETRAVELEDISTHESAME,ANDTHESPEEDOFTHESECONDISALSOKNOWNTHEREFORE,THESPEEDOFANAILCANBECALCULATED,ANDTHEWHOLECOURSEOFTHETWOPLACESCANBECALCULATEDANSWERARMOURSPEED50X2888301928850X36/201800/2090MDISTANCEBETWEENEASTANDWEST9060815081200MANSWEREASTANDWESTARE1200METERSAPART9,AANDB,TWOPEOPLEFROM50KILOMETERSAWAYATTHESAMETIME,THEOPPOSITEDIRECTIONALINEOF6KILOMETERSPERHOUR,BPERHOUR4KM,AWITHADOG,THEDOGRAN12KILOMETERSPERHOUR,THEDOGWITHAWAYOFMEETINGB,ITWILLTURNTOWARDARUNINHERE,ANDTOENCOUNTERABSIDERUN,UNTILTHETWOMEETANDTHEDOGRANATOTALOFHOWMANYKILOMETERSANALYSISFORTHISPROBLEM,AFTERREADING,IFINDITVERYCOMPLICATEDASKTHEDOGTORUNATOTALDISTANCE,ITISNECESSARYTOMEETTHEDOGANDTHESECOND,RUNNINGDISTANCE,METWITHARUNNINGDISTANCE,ANDTHENMETWITHTHERUNNINGOFTHEDISTANCETHEYAREALLWORKEDOUT,ANDTHENSUMMEDUPTOCALCULATETHERESULTBUTTHINKCAREFULLYABOUTHOWMANYTIMESADOGWILLRUNBETWEENAANDB,ANDHOWMUCHTIMEITTAKESTOGOBACKANDFORTHBETWEENTWOPEOPLETHENCAREFULLY,FROMANOTHERPERSPECTIVE,ITISNOTDIFFICULTTOFIND,THEDOGRUNSPEEDMULTIPLIEDBYTHEDISTANCEEQUALTOTHEDOGRUNTIMENOMATTERHOWMANYTIMESTHEDOGRUNSBETWEENAANDB,THETOTALTIMESPENTBYTHEDOGISEQUALTOTHETIMEITTAKESFORATWOORTWOPEOPLETOMEETTHEREFORE,THETIMEREQUIREDFORTHEDOGTORUN,THATIS,TOFINDA,B,TWOPEOPLEENCOUNTERTIMETHEREFORE,THEORIGINALQUESTIONWASTRANSFORMEDINTOTHEPROBLEMOFMEETINGTHETWOPEOPLEATTHETIMEOFSEEKINGAANDBANSWERBTWOMEETINGTIMEIS50