A boat covers 12, km upstream and 18, km down | vedclass

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(C) Let the speed of the boat in still water be $x\, km/h$ and the speed of the current be $y\, km/h$.According to the problem:$\frac{12}{x-y} + \frac

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$2$

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(C) Let the speed of the boat in still water be $x\, km/h$ and the speed of the current be $y\, km/h$.According to the problem:$\frac{12}{x-y} + \frac{18}{x+y} = 3$ $...(1)$$\frac{36}{x-y} + \frac{24}{x+y} = \frac{13}{2}$ $...(2)$Multiply equation $(1)$ by $3$:$\frac{36}{x-y} + \frac{54}{x+y} = 9$ $...(3)$Subtract equation $(2)$ from equation $(3)$:$(\frac{36}{x-y} - \frac{36}{x-y}) + (\frac{54}{x+y} - \frac{24}{x+y}) = 9 - \frac{13}{2}$$\frac{30}{x+y} = \frac{5}{2}$$x+y = 12$ $...(4)$Substitute $x+y = 12$ into equation $(1)$:$\frac{12}{x-y} + \frac{18}{12} = 3$$\frac{12}{x-y} + 1.5 = 3$$\frac{12}{x-y} = 1.5$$x-y = \frac{12}{1.5} = 8$ $...(5)$To find the speed of the current $(y)$,subtract equation $(5)$ from equation $(4)$:$(x+y) - (x-y) = 12 - 8$$2y = 4$$y = 2\, km/h$.

$A$ boat covers $12\, km$ upstream and $18\, km$ downstream in $3\, hours,$ while it covers $36\, km$ upstream and $24\, km$ downstream in $6\frac{1}{2}\, hours.$ What is the speed of the current? (in $km/h$)

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