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

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(C) Let the speed of the boat in still water be $u 	ext{ km/h}$ and the speed of the stream be $v 	ext{ km/h}$.Then,upstream speed $= (u - v) 	ext{

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$2$

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(C) Let the speed of the boat in still water be $u 	ext{ km/h}$ and the speed of the stream be $v 	ext{ km/h}$.Then,upstream speed $= (u - v) 	ext{ km/h}$ and downstream speed $= (u + v) 	ext{ km/h}$.According to the problem:$\frac{24}{u-v} + \frac{36}{u+v} = 6$  --- $(1)$$\frac{36}{u-v} + \frac{24}{u+v} = 6.5 = \frac{13}{2}$ --- $(2)$Let $X = \frac{1}{u-v}$ and $Y = \frac{1}{u+v}$.$24X + 36Y = 6 \Rightarrow 4X + 6Y = 1$ --- $(3)$$36X + 24Y = \frac{13}{2} \Rightarrow 72X + 48Y = 13$ --- $(4)$Multiplying $(3)$ by $8$: $32X + 48Y = 8$ --- $(5)$Subtracting $(5)$ from $(4)$: $40X = 5 \Rightarrow X = \frac{1}{8}$.Substituting $X$ in $(3)$: $4(\frac{1}{8}) + 6Y = 1 \Rightarrow 0.5 + 6Y = 1 \Rightarrow 6Y = 0.5 \Rightarrow Y = \frac{1}{12}$.So,$u - v = 8$ and $u + v = 12$.Adding the two equations: $2u = 20 \Rightarrow u = 10 	ext{ km/h}$.Subtracting the two equations: $2v = 4 \Rightarrow v = 2 	ext{ km/h}$.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 $6.5 \text{ hours}$. The velocity of the current is ......... $\text{km/h}$.

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