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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 speed of boat is u km/hr and stream speed is v km/hr upstream speed= u-v km/hr downstream speed =u+v km/hr distance d=24 km aaplying given condition d/u-v -d/u+v=1 v^2+48v-324=0 solving above quadratic equn.... v=6,-54 since speed of stream can not be negative hence speed of stream v=6...
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speed=distance/time so, time=distance/speed For upstream : t+1=24/18-s (Where s is speed of stream) For downstream : t=24/18+s => (24/18-s)-1=(24/18+s) =>(24/18-s)-(24/18+s)=1 =>s^2+48s-324=0 =>(s+54)(s-6)=0 so, speed of stream=6km/hr.
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Let the speed of stream by x kmph. then speed of boat in water upstream = (18-x) kmph Speed of boat in water downstream = (18+x) kmph Now time = Distance / speed Time taken to go upstream - time taken to go downstream = 1 hr 24/(18-x) - 24/(18+x) = 1 24( 18+x-18+x ) = (18^2 - x2) 48x = 324...
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Let the speed of stream by x kmph. then speed of boat in water upstream = (18-x) kmph Speed of boat in water downstream = (18+x) kmph Now time = Distance / speed Time taken to go upstream - time taken to go downstream = 1 hr 24/(18-x) - 24/(18+x) = 1 24( 18+x-18+x ) = (18^2 - x2) 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, speed of stream (x) = 6kmph read less
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