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Class 10 > Learn Mathematics > A motor boat whose speed is 18 km/h in still water...
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A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

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Let the speed of stream by x km/h. Speed of boat upstream = ( 18- x ) kmph Speed of boat downstream = ( 18+x ) kmph Now time = Distance / Speed Time taken to go upstream - Time taken to go downstream = 1hr 24/(18-x) - 24/(18+x) = 1 -48x = 324 - x2 x2-48x-324 = 0 x2-54x+6x-324=0 x(x-54)+6(x-54)=0 (x+6)(x-54)=0...
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Let the speed of stream by x km/h. Speed of boat upstream = ( 18- x ) kmph Speed of boat downstream = ( 18+x ) kmph Now time = Distance / Speed Time taken to go upstream - Time taken to go downstream = 1hr 24/(18-x) - 24/(18+x) = 1 -48x = 324 - x2 x2-48x-324 = 0 x2-54x+6x-324=0 x(x-54)+6(x-54)=0 (x+6)(x-54)=0 therefore x = 54 ( as x cannot be -6) Speed of the stream is 54kmph read less
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Let, speed of boat in still water =u km/hr, Speed of stream= v km/hr Speed downstream=u+v, speed upstream=u-v. Speed downstream=18+v, Speed upstream=18-v, 24/t=18+v, 24/t+1=18-v, Adding both equations we get, 24/t+(24/t+1)=36 Solving we get quadratic equation 3t^2-3t-2=0. We get t=1 and t=-2/3. As time...
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Let, speed of boat in still water =u km/hr,

Speed of stream= v km/hr

Speed downstream=u+v,

speed upstream=u-v.

Speed downstream=18+v,

Speed upstream=18-v, 24/t=18+v, 24/t+1=18-v,

Adding both equations we get,

24/t+(24/t+1)=36

Solving we get quadratic equation 3t^2-3t-2=0.

We get t=1 and t=-2/3.

As time cannot be negative t=1.

Speed downstream=24/1=24.

Speed upstream=24/2=12

speed of stream=(1/2)*Speed downstream-Speed upstream

=(24-12)/2=6 km/hr.

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6kmph
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Let the speed of stream by x km/h. Speed of boat upstream = ( 18- x ) kmph Speed of boat downstream = ( 18+x ) kmph Now time = Distance / Speed Time taken to go upstream - Time taken to go downstream = 1hr 24/(18-x) - 24/(18+x) = 1 -48x = 324 - x2 x2-48x-324 = 0 x2-54x+6x-324=0 x(x-54)+6(x-54)=0 (x+6)(x-54)=0 therefore...
read more
Let the speed of stream by x km/h. Speed of boat upstream = ( 18- x ) kmph Speed of boat downstream = ( 18+x ) kmph Now time = Distance / Speed Time taken to go upstream - Time taken to go downstream = 1hr 24/(18-x) - 24/(18+x) = 1 -48x = 324 - x2 x2-48x-324 = 0 x2-54x+6x-324=0 x(x-54)+6(x-54)=0 (x+6)(x-54)=0 therefore x = 54 ( as x cannot be -6) Speed of the stream is 54kmph read less
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