Question 9

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

Solution

Let the distance of the station from the house of the person = $$x$$ km

Difference of time = 8 + 7 = 15 minutes = $$\frac{1}{4}$$ hr

Since, Time = $$\frac{Distance}{Speed}$$

$$\therefore \frac{x}{6} - \frac{x}{10} = \frac{1}{4}$$

=> $$\frac{10x - 6x}{60} = \frac{1}{4}$$

=> $$\frac{2x}{30} = \frac{1}{4}$$

=> $$x = \frac{15}{4} = 3\frac{3}{4}$$ km

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