A Motor Boat Whose Speed Is 18 Km/h In Still Water Takes 1 Hour ...

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathsQuestionA 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.Open in AppSolutionVerified by Toppr

Given:- Speed of boat =18km/hrDistance =24kmLet x be the speed of stream.Let t1 and t2 be the time for upstream and downstream.As we know that,speed=distancetime⇒time=distancespeedFor upstream,Speed =(18−x)km/hrDistance =24kmTime =t1Therefore,t1=2418−xFor downstream,Speed =(18+x)km/hrDistance =24kmTime =t2Therefore,t2=2418+xNow according to the question-t1=t2+12418−x=2418+x+1⇒118−x−118+x=124⇒(18+x)−(18−x)(18−x)(18+x)=124⇒48x=(18−x)(18+x)⇒48x=324+18x−18x−x2⇒x2+48x−324=0⇒x2+54x−6x−324=0⇒x(x+54)−6(x+54)=0⇒(x+54)(x−6)=0⇒x=−54 or x=6Since speed cannot be negative.⇒x≠−54∴x=6Thus the speed of stream is 6km/hrHence the correct answer is 6km/hr.

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