If a man walks at the rate of 4 km/hr, he misses a train by only 6 minutes. However, if he walks at the rate of 5 km/hr,he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is:
Explanation
Given:
Speed of the man when he is 6 minutes late = 4 km/hr
Speed of the man when he is 6 minutes before = 5 km/hr
Concept used:
Distance = Speed × Time
1 min = 1/60 hrs
Calculation:
Let the correct time of train arrival be t and distance to reach the station be d.
⇒ d = 4 × (t + 6)/60 ----(1)
⇒ d = 5 × (t – 6)/60 ----(2)
From equations (1) and (2),
⇒ 4 × (t + 6)/60 = 5 × (t – 6)/60
⇒ 4t + 24 = 5t – 30
⇒ 5t – 4t = 30 + 24
⇒ t = 54 min
Putting the value of t in equation (1),
⇒ d = 4 × (54 + 6)/60
⇒ 4 × 60/60
⇒ 4 km
∴The distance covered by him to reach the station is 4 km.
