The current of a stream runs at the rate of 4 | vedclass

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Question

(B) Let the speed of the boat in still water be $x 	ext{ km/h}$.Given,speed of the stream $= 4 	ext{ km/h}$.Speed downstream $= (x + 4) 	ext{ km/h}

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) Let the speed of the boat in still water be $x 	ext{ km/h}$.Given,speed of the stream $= 4 	ext{ km/h}$.Speed downstream $= (x + 4) 	ext{ km/h}$ and speed upstream $= (x - 4) 	ext{ km/h}$.Time taken to travel $6 	ext{ km}$ downstream $= \frac{6}{x + 4} 	ext{ hours}$.Time taken to travel $6 	ext{ km}$ upstream $= \frac{6}{x - 4} 	ext{ hours}$.According to the problem,the total time is $2 	ext{ hours}$:$\frac{6}{x + 4} + \frac{6}{x - 4} = 2$Divide by $2$: $\frac{3}{x + 4} + \frac{3}{x - 4} = 1$$3(x - 4) + 3(x + 4) = (x + 4)(x - 4)$$3x - 12 + 3x + 12 = x^2 - 16$$6x = x^2 - 16$$x^2 - 6x - 16 = 0$$(x - 8)(x + 2) = 0$Since speed cannot be negative,$x = 8 	ext{ km/h}$.

The current of a stream runs at the rate of $4 \text{ km/h}$. $A$ boat goes $6 \text{ km}$ and comes back to the starting point in $2 \text{ hours}$. The speed of the boat in still water is ....... $\text{km/h}$.

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