A thief is spotted by a policeman from a distance of 100 m. The thief starts running and the policeman chases him. If the speed of thief and policeman are 21 km/h and 23 km/h, respectively, then how far will the thief have to run before he is overtaken?

Question

Accepted Answer

Given:
- Initial distance between policeman and thief = 100 m
- Speed of thief = 21 km/h
- Speed of policeman = 23 km/h

Step 1: Convert speeds from km/h to m/s
1 km/h = 1000 m / 3600 s = 5/18 m/s

Speed of thief = 21 × 5/18 = 35/6 m/s
Speed of policeman = 23 × 5/18 = 115/18 m/s

Step 2: Calculate relative speed of policeman with respect to thief
Relative speed = Speed of policeman - Speed of thief
= (115/18) - (35/6)
= (115/18) - (105/18) = 10/18 = 5/9 m/s

Step 3: Calculate time taken to catch the thief
Time = Distance / Relative speed = 100 / (5/9) = 100 × (9/5) = 180 seconds

Step 4: Calculate distance run by thief in this time
Distance = Speed × Time = (35/6) × 180 = 35 × 30 = 1050 m

Therefore, the thief will have to run 1050 meters before he is overtaken.

Answer

Answer

Answer