Question 188902: A boat took 1 hour and 50 minutes to go 55 km downstream and 3 hours, 40 minutes to return. Find the boats rate in still water and the rate of the current?
downstream data:
distance=55km; time= (11/6) hr.; rate=d/t= 55/(11/6= 30 kph
need to know how 1 hour and 50 minutes changes to 11/6 of an hr? and how does 55/(11/6)= 30?
up stream data:
distance= 55 km; time= (11/3)hr. rate= d/t= 55/(11/3)=15 kph
need to know how 3 hours and 40 minutes = (11/3)of an hour and how does 55/(11/3)=15 kph?
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! Let r=speed of boat in still water, c=speed of current, t=time, d=distance
rt=d
110(r+c)=55
220(r-c)=55
.
110r+110c=55
220r-220c=55
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220r+220c=110 multiply the 1st equation by 2
220r-220c==55
--------------add
440r======165
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r=.375 kpm
.
110(.375+c)=55
41.25+110c=55
110c=13.75 kpm
c=.125 kpm
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r=.375*60=22.5 kph
c=.125*60=7.5 kph
.
Ed
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