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Q.

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 ?

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a

\frac{3}{4} km

b

\frac{4}{5} km

c

\frac{5}{4} km

d

1 km

answer is B.

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Detailed Solution

Let x be the distance which I walk to reach the station
We know that time =

\frac{distance}{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{4 x - 3 x}{12} = \frac{- 2}{30}

⇒

\frac{x}{12} = \frac{- 1}{15}

⇒

x = \frac{- 12}{15} = \frac{- 4}{5} km

Since distance cannot be negative
⇒

x = \frac{4}{5} km

The correct option is 3
Basic Algebraic Identities

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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 ?