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Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(u-v)] km/h
where u= speed of boat in downstream
v=speed of boat in upstream
Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(u-v)] km/h
where u= speed of boat in downstream
v=speed of boat in upstream
Speed of boat in still water=[(1/2)(7+13)] =10 km/h
Speed of the stream =[(1/2)(13-7)]=3 km/h
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Let the speed of the stream = x km/h
∴ Speed of boat in still water = 10 km/h
Speed of boat downstream = (x + 10) km/h
Speed of boat upstream=(10 - x) km/h
Let the speed of the stream = x km/h
∴Speed of boat in still water = 10 km/h
Speed of boat downstream = ( x + 10) km/h
Speed of boat upstream=(10 - x) km/h
∴ Time taken to travel 26 km downstream=[ 26 / ( 10 + x ) ] h
Time taken to travel 14 km upstream=[ 14 /( 10 - x )] h
⇒ By condition [ 26 / ( 10 + x)]=[ 14 / ( 10 - x)]
⇒ 26(10-x)=14(10+x)
⇒ 260-26x =140 + 14x
⇒ 40x=120
⇒ x = 3 Here, speed of stream = 3 km/h
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Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr
Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.
Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr
Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.
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Let the rate against the current be x km/hr.
Then, (12 - x) / 2 = 1.5
Let the rate against the current be x km/hr.
Then, (12 - x) / 2 = 1.5
⇒ 12 - x = 3
⇒ x = 9 km/hr
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Speed of current = 5 - 3.5 = 1.5 km/hr.
Speed of current = 5 - 3.5 = 1.5 km/hr.
So the speed of man along the current = 5 + 1.5 = 6.5 km/hr