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
Step-by-step Solution:
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.