A boat travels upstream from B to A and downs | vedclass

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Question

(B) Let the distance between $A$ and $B$ be $x\, km$.Speed of the boat in still water $= 9\, km/h$.Speed of the current $= 3\, km/h$.Upstream speed $=

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) Let the distance between $A$ and $B$ be $x\, km$.Speed of the boat in still water $= 9\, km/h$.Speed of the current $= 3\, km/h$.Upstream speed $= (	ext{Speed of boat} - 	ext{Speed of current}) = 9 - 3 = 6\, km/h$.Downstream speed $= (	ext{Speed of boat} + 	ext{Speed of current}) = 9 + 3 = 12\, km/h$.Time taken to travel upstream from $B$ to $A = \frac{x}{6}\, hours$.Time taken to travel downstream from $A$ to $B = \frac{x}{12}\, hours$.According to the problem, the total time taken is $3\, hours$:$\frac{x}{6} + \frac{x}{12} = 3$To solve for $x$, find a common denominator:$\frac{2x + x}{12} = 3$$\frac{3x}{12} = 3$$\frac{x}{4} = 3$$x = 12\, km$.Thus, the distance between $A$ and $B$ is $12\, km$.

$A$ boat travels upstream from $B$ to $A$ and downstream from $A$ to $B$ in $3$ $hours$. If the speed of the boat in still water is $9\, km/h$ and the speed of the current is $3\, km/h$, find the distance between $A$ and $B$ in kilometres.

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