Question

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?

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

Answer 1

Answer: (B)

$\frac{4}{5}$ km

Let the distance which I walk to the station be x km Then Time needed to reach the station at 3 km/hr = $(\frac{x}{3}+\frac{2}{60})$ hrs and
Time needed to reach the station at 4 km/hr = $(\frac{x}{4}+\frac{2}{60})$ hrs But $\frac{x}{3}+\frac{1}{30}=\frac{x}{4}-\frac{1}{30}\Rightarrow \frac{x}{3}-\frac{x}{4}=-\frac{2}{30}=\frac{1}{15}$
$\Rightarrow \frac{4x-3x}{12}=\frac{1}{15}\Rightarrow \frac{x}{12}=\frac{1}{15}\Rightarrow x=\frac{12}{15}=\frac{4}{5}$ km