the speed of a boat in still water is 11 km/hr.it can go 10km upstream and return downstream in 2 hrs45mins. find the speed of the stream
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Speed of the boat in still water = 11 km/h
Distance (One way) = 10 km
Time taken (both ways) = 2 hours 45 mins = 2.75 hours
Define x:
Let the speed of the stream be x
Upstream:
Speed = (11 - x) km/h
Time = Distance ÷ speed
Time = 10/(11 - x) hours
Downstream:
Speed = ( 11 + x ) km/h
Time = Distance ÷ Speed
Time = 10 / ( 11 + x) hours
Solve x:
Given that the total time = 2.75 hours
10/ (11 - x) + 10/( 11 + x) = 2.75
10(11 + x) + 10( 11 - x) = 2.75 (11 - x)(11 + x)
110 + 10x + 110 - 10x = 2.75 (121 - x²)
110 + 10x + 110 - 10x = 332.75 - 2.75x²
220 = 332.75 - 2.75x²
2.75x² = 332.75 - 220
2.75x² = 112.75
x² = 41
x = √41
x = 6.4 km/h
Answer: The speed of the stream is 6.4 km/h
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