If a man runs at 6 kmph from his house, he misses the train at the station by 8 min. If he runs at 10 kmph, he reaches 7 min before the departure of the train. What is the distance of the station from his house? (in Km).

Explanation:-

Let the distance of the station from the house of the person = x km $$\eqalign{ & {\text{Difference}}\,{\text{of}}\,{\text{time}} \cr & = 8 + 7 \cr & = 15\,{\text{minutes}} \cr & = \frac{1}{4}\,hr \cr & {\text{Since}},\, \cr & {\text{Time}} = \frac{{{\text{Distance}}}}{{{\text{Speed}}}} \cr & \therefore \frac{x}{6} - \frac{x}{{10}} = \frac{1}{4} \cr & \Rightarrow \frac{{10x - 6x}}{{60}} = \frac{1}{4} \cr & \Rightarrow \frac{{2x}}{{30}} = \frac{1}{4} \cr & \Rightarrow x = \frac{{15}}{4} = 3\frac{3}{4}km \cr}$$