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A train covers a certain distance at a uniform speed. If the train had been $6$ kilometre per hour faster, it would have taken $4$ hour less than the scheduled time and if the train was slower by $6$ kilometre per hour it would have taken $6$ hour more than the schedule time. Find length of the journey. 0 0 comment dev

## Solution 1

Refer formula

Speed $=\dfrac{6×6(4+6)}{6×6-6×4}=30\text{ km/hr}$

Required distance $=30×4\left(1+\dfrac{30}{6}\right)=720\text{ km}$

## Solution 2

Let distance and speed be $x$ km and $v$ km/hr respectively. From the given statements, we can form the following equations.

$\dfrac{x}{v}-\dfrac{x}{v+6}=4\cdots(1)$

$\dfrac{x}{v-6}-\dfrac{x}{v}=6\cdots(2)$

solving these equation yields, $x=720$ and $v=30$

That is, required distance is $720$ km

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