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(A) Let the distance between station $A$ and station $B$ be $x \, km$.Let the initial speed of the train be $v \, km/h$.Time taken in the first case i

Vedclass · Accepted Answer

$60$

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(A) Let the distance between station $A$ and station $B$ be $x \, km$.Let the initial speed of the train be $v \, km/h$.Time taken in the first case is $45 \, min = \frac{45}{60} \, h = \frac{3}{4} \, h$.So,$x = v 	imes \frac{3}{4} \Rightarrow v = \frac{4x}{3}$.Time taken in the second case is $48 \, min = \frac{48}{60} \, h = \frac{4}{5} \, h$.The new speed is $(v - 5) \, km/h$.So,$x = (v - 5) 	imes \frac{4}{5} \Rightarrow v - 5 = \frac{5x}{4} \Rightarrow v = \frac{5x}{4} + 5$.Equating the two expressions for $v$:$\frac{4x}{3} = \frac{5x}{4} + 5$.$\frac{4x}{3} - \frac{5x}{4} = 5$.$\frac{16x - 15x}{12} = 5$.$\frac{x}{12} = 5 \Rightarrow x = 60 \, km$.

$A$ train covers a distance between station $A$ and station $B$ in $45 \, min$. If the speed of the train is reduced by $5 \, km/h$,then the same distance is covered in $48 \, min$. The distance between stations $A$ and $B$ is? (in $km$)

Similar Questions

$A$ train covers a distance between station $A$ and station $B$ in $45\, minutes.$ If the speed of the train is reduced by $5\, km/h,$ then the same distance is covered in $48\, minutes.$ The distance between stations $A$ and $B$ is (in $km$):

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