A boat covers 24 text{ km} upstream and 36 te | vedclass

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(A) Let $u$ be the upstream speed and $v$ be the downstream speed in $	ext{km/h}$.From the given information:$\frac{24}{u} + \frac{36}{v} = 6 \quad \

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(A) Let $u$ be the upstream speed and $v$ be the downstream speed in $	ext{km/h}$.From the given information:$\frac{24}{u} + \frac{36}{v} = 6 \quad \dots (i)$$\frac{36}{u} + \frac{24}{v} = \frac{13}{2} \quad \dots (ii)$Multiply equation $(i)$ by $3$ and equation $(ii)$ by $2$:$\frac{72}{u} + \frac{108}{v} = 18 \quad \dots (iii)$$\frac{72}{u} + \frac{48}{v} = 13 \quad \dots (iv)$Subtracting $(iv)$ from $(iii)$:$\frac{60}{v} = 5 \implies v = 12 	ext{ km/h}$.Substitute $v = 12$ into $(i)$:$\frac{24}{u} + \frac{36}{12} = 6 \implies \frac{24}{u} + 3 = 6 \implies \frac{24}{u} = 3 \implies u = 8 	ext{ km/h}$.Let $x$ be the speed of the boat in still water and $y$ be the velocity of the current.$x - y = 8$ and $x + y = 12$.Adding the two equations: $2x = 20 \implies x = 10 	ext{ km/h}$.Subtracting the two equations: $2y = 4 \implies y = 2 	ext{ km/h}$.Thus,the velocity of the current is $2 	ext{ km/h}$.

$A$ boat covers $24 \text{ km}$ upstream and $36 \text{ km}$ downstream in $6 \text{ hours}$,while it covers $36 \text{ km}$ upstream and $24 \text{ km}$ downstream in $6 \frac{1}{2} \text{ hours}$. The velocity of the current is .... $\text{km/h}$.

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