Solution:
Given:
Initial distance between thief and policeman = 500 m
Speed of thief = 8 km/h
Speed of policeman = 11 km/h
Concept used:
Relative speed and time = distance/speed
Solution:
Relative speed = speed of policeman - speed of thief = 11 km/h - 8 km/h = 3 km/h = 3 × (1000/3600) m/s = 5/6 m/s
Time taken to catch the thief = initial distance / relative speed
Time taken to catch the thief = 500 m / (5/6 m/s) = 600 seconds
Distance run by the thief before he was caught = Speed of thief × time = (8 × 1000/3600) m/s × 600 s = 1333.33 meters
Therefore, the distance run by the thief before he was caught is approximately 1333.33 meters.
Shortcut Trick
Here, the thief and the police is running for the same time. So, time = constant.
When time is constant Speed ∝ Distance
Distance between the thief and the police = 3 unit = 500 km
⇒ 1 unit = 500/3
⇒ 8 unit = (500 × 8)/3 = 1333.33 m
Therefore, the distance run by the thief before he was caught is approximately 1333.33 meters.
