A motor-boat,travelling at the same speed,can | vedclass

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(C) Let the speed of the motorboat in still water be $x\, km/h$ and the speed of the stream be $y\, km/h$.According to the problem:$\frac{25}{x-y} + \

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$4$

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(C) Let the speed of the motorboat in still water be $x\, km/h$ and the speed of the stream be $y\, km/h$.According to the problem:$\frac{25}{x-y} + \frac{39}{x+y} = 8$ $...(1)$$\frac{35}{x-y} + \frac{52}{x+y} = 11$ $...(2)$Let $u = \frac{1}{x-y}$ and $v = \frac{1}{x+y}$.The equations become:$25u + 39v = 8$ $...(3)$$35u + 52v = 11$ $...(4)$Multiply equation $(3)$ by $4$ and equation $(4)$ by $3$:$100u + 156v = 32$ $...(5)$$105u + 156v = 33$ $...(6)$Subtracting $(5)$ from $(6)$:$5u = 1 \Rightarrow u = \frac{1}{5}$.Since $u = \frac{1}{x-y}$,we have $x-y = 5$.Substitute $u = \frac{1}{5}$ into equation $(3)$:$25(\frac{1}{5}) + 39v = 8$$5 + 39v = 8 \Rightarrow 39v = 3 \Rightarrow v = \frac{1}{13}$.Since $v = \frac{1}{x+y}$,we have $x+y = 13$.Solving $x-y = 5$ and $x+y = 13$:Adding the two equations: $2x = 18 \Rightarrow x = 9$.Subtracting the two equations: $2y = 8 \Rightarrow y = 4$.Thus,the speed of the stream is $4\, km/h$.

$A$ motor-boat,travelling at the same speed,can cover $25\, km$ upstream and $39\, km$ downstream in $8\, hours$. At the same speed,it can travel $35\, km$ upstream and $52\, km$ downstream in $11\, hours$. The speed of the stream is $........\, km/h$.

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