The speed of the flow of a river is 3 , km/hr | vedclass

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(D) Let the speed of the motorboat in still water be $x \, km/hr$.Therefore,the speed of the motorboat going downstream is $(x+3) \, km/hr$ and its sp

Vedclass · Accepted Answer

$9$

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(D) Let the speed of the motorboat in still water be $x \, km/hr$.Therefore,the speed of the motorboat going downstream is $(x+3) \, km/hr$ and its speed going upstream is $(x-3) \, km/hr$.Hence,the time taken to cover $12 \, km$ downstream is $\frac{12}{x+3}$ hours and the time taken to cover the same distance,i.e.,$12 \, km$ to come back upstream is $\frac{12}{x-3}$ hours.According to the problem,the total time taken is $3$ hours.$\frac{12}{x+3} + \frac{12}{x-3} = 3$$12(x-3) + 12(x+3) = 3(x+3)(x-3)$$12x - 36 + 12x + 36 = 3(x^2 - 9)$$24x = 3x^2 - 27$$3x^2 - 24x - 27 = 0$Dividing by $3$,we get $x^2 - 8x - 9 = 0$.$(x-9)(x+1) = 0$$x = 9$ or $x = -1$.Since the speed cannot be negative,$x = 9 \, km/hr$.

The speed of the flow of a river is $3 \, km/hr$. $A$ motorboat goes $12 \, km$ downstream and comes back in a total time of $3$ hours. Find the speed of the motorboat in still water. (The speed of flow of water is less than the speed of the boat.)

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