If I walk at 3 km/hr. I miss a train by 2 minutes, if however I walk at 4 km/hr then I reach the station 2 minutes before the arrival of the train. How far do I walk to reach the station ?

# If I walk at 3 km/hr. I miss a train by 2 minutes, if however I walk at 4 km/hr then I reach the station 2 minutes before the arrival of the train. How far do I walk to reach the station ?

1. A
$\frac{3}{4}\mathit{km}$
2. B
$\frac{4}{5}\mathit{km}$
3. C
$\frac{5}{4}\mathit{km}$
4. D
$1\mathit{km}$

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### Solution:

Let x be the distance which I walk to reach the station
We know that time = $\frac{\mathit{distance}}{\mathit{Speed}}$
Therefore when I walk at a speed of 3 km/hr I reach the station 2 minutes late
T=($\frac{x}{3}+\frac{2}{60}$) ……….(1)
Here the extra 2 minutes is written as  $\frac{2}{60}$ because our calculation in done in terms of hours so we convert minutes to hours by dividing it by 60
Here we add the two minutes as I take two minutes extra (in addition )
Therefore when I walk at a speed of 4 km/hr I reach the station 2 minutes early
T=($\frac{x}{4}-\frac{2}{60}$)……….(2)
Here we subtract the two minutes as I reach 2 minutes earlier
Equating (1) and (2)
($\frac{x}{3}+\frac{2}{60}$) =($\frac{x}{4}-\frac{2}{60}$)
($\frac{x}{3}-\frac{x}{4}$)= $\frac{-1}{30}-\frac{1}{30}$
$\frac{4x-3x}{12}=\frac{-2}{30}$
$\frac{x}{12}=\frac{-1}{15}$
$x=\frac{-12}{15}=\frac{-4}{5}\mathit{km}$
Since distance cannot be negative
$x=\frac{4}{5}\mathit{km}$
The correct option is 3
Basic Algebraic Identities

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