boats and streams
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boat and streamTRANSCRIPT
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BoatsandStreams
AllthebasicconceptsofTimespeedandDistanceapplytothischapterBoatsandstreams.Wehavetoadjustthespeedsaccordingtothepointwhethertheboatismovingagainstthestreamorwiththestream.
Therearetwoparametersintheseproblems.
1.SpeedoftheStream(S):Thisisthespeedwithwhichtheriverflows.2.Speedoftheboatinstillwater(B):Iftheriverisstill,thisisthespeedatwhichtheboatwouldbemoving.
Theeffectivespeedofaboatinupstream=BSTheeffectivespeedofaboatindownstream=B+S
3.ThespeedoftheboatinstillwaterisgivenasB= ,andthespeedoftheStreamS= ,
wheredanduarethedownstreamandupstreamspeeds,respectively.
SolvedExamples
1.Agirlcanswim3km/hrinstillwater.Ifthevelocityofthestreambe2km/hrthetimetakenbyhertoswimtoaplace10kmupstreamandbackis:
a. hrs
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b. hr
c.10hrsd.12hrsCorrectOption:DExplanation:Speedofupstream=(32)km/hr=1km/hrSpeedofdownstream(3+2)km/hr=5km/hr
Totaltimetaken= hrs=12hrs
2.Agirlcanrowthreequartersofakilometeragainstthestreamin minutesandreturnin minutes.The
speedofthegirlinstillwateris:a.2km/hrb.3km/hrc.4km/hrd.5km/hrCorrectOption:DExplanation:
Speedofupstream= = km/hr=4km/hr
Speedofdownstream= = km/hr=6km/hr
Speedinstillwater= km/hr=5km/hr
3.Agirlcanrow km/hrinstillwaterandshefindsthatittakesherthriceasmuchtimetorowupthanastorow
downthesamedistanceinriver.Thespeedofthecurrentis:
a. km/hr
b. km/hr
c. km/hr
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d. km/hr
CorrectOption:DExplanation:Letspeedofupstream=xkm/hrThen,speedofdownstream=3xkm/hr
Speedinstillwater= km/hr=2xkm/hr
Speedofthecurrent= km/hr=xkm/hr
orx= km/hr
4.Thecurrentofastreamrunsat1km/hr.Amotorboatgoes35km.upstreamandbackagaintothestartingpointin12hours.Thespeedofmotorboatinstillwateris:a.6km/hrb.7km/hrc.8.5km/hrd.8km/hrCorrectOption:AExplanation:Letthespeedinstillwaterbexkm/hr.
or35(2x)=12ororor12x(x6)+2(x6)=0or(x6)(12x+2)=0x=6km/hr
5.Amotorcovers24kmupstreamand36kmdownstreamin6hours,whileitcovers36kmupstreamand24km
downstreamin hours.Thevelocityofthestreamis:
a.1.5km/hr
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b.1km/hrc.2km/hrd.2.5km/hrCorrectOption:CExplanation:Letthespeedofupstreambexkm/hrandthespeedofdownstreambeykm/hr.Then,
,whereu=1/x,v=1/y
And,
Addingtheseequations,weget oru+v=
Subtracting,weget oruv=
Solvingu+v= anduv= wegetu= andv=
x=8km/hrory=12km/hr
Velocityofcurrent= (128)km/hr=2km/hr
6.Thecurrentofstreamrunsattherateof4kmanhour.Aboatgoes6kmandbacktothestartingpointin2hours.Thespeedoftheboatinstillwateris:a.6km/hrb.7.5km/hrc.8km/hrd.6.8km/hrCorrectOption:CExplanation:Letthespeedinstillwaterbexkm/hr
Then,
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or(x8)(x+2)=0.So,x=8km/hr
7.Amanrowstoaplace48kmdistantandbackin14hours.Hefindsthathecanrow4kmwiththestreaminthesametimeas3kmagainstthestream.Therateofthestreamis:a.0.5km/hrb.1km/hrc.3.5km/hrd.1.8km/hrCorrectOption:BExplanation:Supposehemoves4kmdownstreaminxhours
Then,speedofdownstream= km/hr
Speedofupstream= km/hr
Speedofdownstream=8km/hrSpeedofupstream=6km/hr
Rateofstream= km/hr=1km/hr
8.Aboatmovesupstreamattherateof1kmin10minutesanddownstreamattherateof1kmin6minutes.Thespeedofthecurrentis:a.1km/hrb.1.5km/hrc.2km/hrd.2.5km/hrCorrectOption:CExplanation:Speedofupstream=6km/hrSpeedofdownstream=10km/hr
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Speedofthecurrent= km/hr=2km/hr
9.Agirlrowsupstream16kmanddownstream28km,taking5hourseachtime.Thevelocityofthecurrentis:a.2.4km/hrb.1.2km/hrc.3.6km/hrd.1.8km/hrCorrectOption:BExplanation:
Speedofdownstream= km/hr=5.6km/hr
Speedofupstream= km/hr=3.2km/hr
Velocityofcurrent= km/hr
=1.2km/hr
10.Speedofaboatinstandingwateris6km/hrandthespeedofthestreamis1.5km/hr.Amanrowstoaplaceatadistanceof22.5kmandcomesbacktothestartingpoint.Thetotaltimetakenbyhim,is:a.6hrs30minb.8hrs24minc.8hrsd.4hrs12minCorrectOption:CExplanation:Speedofupstream=(61.5)km/hr=4.5km/hrSpeedofdownstream==(6+1.5)km/hr=7.5km/hr
Totaltimetaken= hrs=8hrs.
11.Amancanrowat5km/hrinstillwaterandthevelocityofcurrentis1km/hr.Ittakeshim1hourtorowtoaplaceandback.Howfaristheplace?a.2.5kmb.2.4km
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c.3kmd.3.6kmCorrectOption:BExplanation:Speedofdownstream=(5+1)km/hr=6km/hrSpeedofupstream=(51)km/hr=4km/hrLettherequireddistancebexkm.
Then,
orx=2.4km
12.AboattravelsupstreamfromQtoPanddownstreamfromPtoQin3hours.Ifthespeedoftheboatinstillwateris9km/hrandthespeedofthecurrentis3km/hr,thedistancebetweenPandQis:a.4kmb.6kmc.8kmd.12kmCorrectOption:DExplanation:Speedofdownstream=(9+3)km/hr=12km/hrSpeedofupstream=(93)km/hr=6km/hrLetthedistanceAB=xkm
Then,
2x+x=36\Rightarrowx=12$DistanceAB=12km.
13.Amotorgoes40kmupstreamin8hoursand36kmdownstreamin6hours.Thespeedoftheboatinstandingwateris:a.6.5km/hrb.6km/hrc.5.5km/hrd.5km/hrCorrectOption:C
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Explanation:
Speedofupstream= km/hr=5km/hr
Speedofdownstream= km/hr=6km/hr
Speedofboatinstillwater
= km/hr=5.5km/hr
14.Ifaman'smovingratewiththecurrentis12km/hrandtherateofthecurrentis1.5km/hr,thenman'smovingrateagainstthestreamis:a.9km/hrb.6.75km/hrc.5.25km/hrd.7.5km/hrCorrectOption:AExplanation:Lettherateagainstthecurrentbexkm/hrThen,
km/hr
15.Ifamanrowsat5km/hrinstillwaterand3.5km/hragainstthecurrent,hisratealongthecurrentis:a.8.5km/hrb.6.5km/hrc.6km/hrd.4.25km/hrCorrectOption:BExplanation:Lettheratealongthecurrentbexkm/hr
Then, =6.5km/hr
16.Thespeedofaboatdownstreamis15km/hrandthespeedofthestreamis1.5km/hr.Thespeedoftheboatupstreamis:a.13.5km/hrb.16.5km/hr
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c.12km/hrd.8.25km/hrCorrectOption:CExplanation:Letthespeedofboatinstillwaterbexkm/hrThen,x+1.5=15 x=13.5Speedofupstream=(13.51.5)km/hr=12km/hr
17.Thespeedofaboatinstillwateris2km/hr.Ifitsspeedupstreambe1km/hr.thenspeedofthestreamis:a.1.5km/hrb.3km/hrc.1km/hrd.NoneoftheseCorrectOption:CExplanation:Letthespeedofstreambexkm/hrThen,speedofupstream=(2x)km/hr2x=1 x=1km/hr
18.Amancanrowdownstreamat14km/hrupstreamat9km/hr.Man'srateinstillwaterisa.5km/hrb.23km/hrc.11.5km/hrd.NoneoftheseCorrectOption:CExplanation:
Man'srateinstillwater= km/hr=
11.5km/hr
19.Agirlcanrowwiththestreamat11km/hrandagainstthestreamat8km/hr.Thespeedofthestreamis:a.3km/hrb.9.5km/hr
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c.1.5km/hrd.6km/hrCorrectOption:CExplanation:
Speedofstream= km/hr=1.5km/hr
20.Ifamanrowsattherateof5kmphinstillwaterandhisrateagainstthecurrentis3.5kmph,thentheman'sratealongwithcurrentis:a.4.25kmphb.6kmphc.6.5kmphd.8.5kmphCorrectOption:CExplanation:Lettheratealongthecurrentbexkmph
Then, =5orx=6.5KMPH.
AdditionalQuestions:
21.Amanrows27kmdownstreamand18kmupstreamtaking3hreachtime.Whatisthevelocityofthecurrent?
Ratedownstream= =9km/hr
Rateupstream= =6km/hr
Velocityofcurrent= (96)=1.5km/hr.
22.Amancanrowupstreamat7km/hranddownstreamat10km/hr.Findhisrateinstillwaterandtherateofthecurrent.
Rateinstillwater= =0.5(10+7)=8.5km/hr
Rateofcurrent= 0.5(107)=1.5km/hr
23.AmanrowsaboatfrompointAagainstcurrentfor10minutesandthencomebackwiththecurrentfornext
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10minutesandreachestoapointB.IfdistancebetweenAandBis1km,findthespeedofthecurrent.Goingwithcurrentandagainstcurrentforthesametimemeansspeedoftheboatinstillwaterisneutralized.Speedofcurrentonlymovestheboat.
Boatismoved1kmbythecurrentin(10+10)minutes=20minute= hour.
Therefore,Speedofcurrent=1x3=3km/h.
24.Amancanrowaboatat6km/hinstillwaterandspeedofthecurrentis2km/h.Ifhetakes45minutestorowtheboattoaplaceandback.Findthedistancebetweenthetwoplaces.Speedoftheboatdownstream=6+2=8km/hSpedoftheboatupstream=62=4km/h
Therefore,Averagespeed= km/h
Timetaken=45minute= hour= hour
25.Amanrowsboattoaplacecovering72kmdistanceandbackin15hours.Hefindsthathecanrow3kmwiththestreaminthesametimeas2kmagainstthestream.Findthespeedofthestream.Speeddownstream:Speedupstream=3:2Therefore,Timetakentorowdownstream:Timetakentorowupstream=2:3But,totaltimetaken=15hours.
Therefore,Timetakentorowdownstream= x15hours=6hours
And,timetakentorowupstream=156=9hours
Therefore,Speeddownstream= =12km/h
And,speedupstream= =8km/h
Therefore,Speedofthestream= =2km/h
AlternativeMethod:Let,downstreamandupstreamspeedsare3km/hand2km/hrespectively.
Then,distancecoveredin15hours= =36km
But,actualdistancecovered=2x72km=144km(i.e.4times36km)Therefore,Speedsare4x3=and4x2,i.e.12and18km/h
Therefore,Speedofthestream= =2km/h
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