A boat goes 24 , km upstream and 28 , km down | vedclass

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(D) Let the speed of the boat in still water be $x \, km/hr$ and the speed of the stream be $y \, km/hr$.Upstream speed $= (x - y) \, km/hr$ and downs

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$10$

Vedclass · Answer

(D) Let the speed of the boat in still water be $x \, km/hr$ and the speed of the stream be $y \, km/hr$.Upstream speed $= (x - y) \, km/hr$ and downstream speed $= (x + y) \, km/hr$.According to the problem:$1) \frac{24}{x-y} + \frac{28}{x+y} = 6$$2) \frac{30}{x-y} + \frac{21}{x+y} = 6.5 = \frac{13}{2}$Let $u = \frac{1}{x-y}$ and $v = \frac{1}{x+y}$.$24u + 28v = 6 \implies 12u + 14v = 3$ (Equation $i$)$30u + 21v = \frac{13}{2} \implies 60u + 42v = 13$ (Equation $ii$)Multiply equation $i$ by $3$: $36u + 42v = 9$ (Equation $iii$)Subtract equation $iii$ from $ii$: $(60u - 36u) = 13 - 9 \implies 24u = 4 \implies u = \frac{1}{6}$.Substitute $u = \frac{1}{6}$ in equation $i$: $12(\frac{1}{6}) + 14v = 3 \implies 2 + 14v = 3 \implies 14v = 1 \implies v = \frac{1}{14}$.So,$x - y = 6$ and $x + y = 14$.Adding the two equations: $2x = 20 \implies x = 10 \, km/hr$.

$A$ boat goes $24 \, km$ upstream and $28 \, km$ downstream in $6 \, hours$. It goes $30 \, km$ upstream and $21 \, km$ downstream in $6 \, hours$ and $30 \, minutes$. The speed of the boat in still water is $...... \, km/hr$.

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