If a man walks at the rate of 4 kmph , he misses a train by only 6 min . However if he walks at the rate of 5 kmph he reaches the station 6 minutes before the arrival of the tain. The distance covered by him to reach the station is
The key to solving this problem is to focus on the difference in travel time between the two scenarios.
- In the first scenario, the man arrives 6 minutes late.
- In the second scenario, he arrives 6 minutes early.
- The total time gap between these two outcomes is 6 + 6 = 12 minutes.
Since the speeds are in km/hr, we need to convert this time difference to hours:
12 minutes = 12/60 = 1/5 of an hour.
- Let the distance to the station be D km.
- We know that Time = Distance / Speed. We can write the time difference as an equation:
(Time at 4 kmph) - (Time at 5 kmph) = 1/5 hour
(D / 4) - (D / 5) = 1/5
- To solve for D, we find a common denominator (20) for the left side of the equation:
(5D / 20) - (4D / 20) = 1/5
D / 20 = 1/5
D = 20 / 5
D = 4 km
Final Answer: The distance covered by him to reach the station is 4 km.
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