The current of a stream runs at 1 , km/h. A m | vedclass

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(B) Let the speed of the motor boat in still water be $x \, km/h$.Given,speed of the stream $= 1 \, km/h$.Speed upstream $= (x - 1) \, km/h$.Speed dow

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(B) Let the speed of the motor boat in still water be $x \, km/h$.Given,speed of the stream $= 1 \, km/h$.Speed upstream $= (x - 1) \, km/h$.Speed downstream $= (x + 1) \, km/h$.Total time taken for the round trip is $12 \, hours$ for a distance of $35 \, km$ each way.Time taken upstream $+$ Time taken downstream $= 12$.$\frac{35}{x - 1} + \frac{35}{x + 1} = 12$.$35 \left( \frac{x + 1 + x - 1}{x^2 - 1} \right) = 12$.$35 \left( \frac{2x}{x^2 - 1} \right) = 12$.$70x = 12(x^2 - 1)$.$12x^2 - 70x - 12 = 0$.Dividing by $2$: $6x^2 - 35x - 6 = 0$.$6x^2 - 36x + x - 6 = 0$.$6x(x - 6) + 1(x - 6) = 0$.$(6x + 1)(x - 6) = 0$.Since speed cannot be negative,$x = 6 \, km/h$.

The current of a stream runs at $1 \, km/h$. $A$ motor boat goes $35 \, km$ upstream and back again to the starting point in $12 \, hours$. The speed of the motor boat in still water in $km/h$ is:

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