A thief is spotted by a policeman from a distance of 200 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 9 km/h and that of the policeman 10 km/h, how far will the thief have to run before he is overtaken?

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Step 1: Convert speeds from km/h to m/s.  
- Speed of thief = 9 km/h = (9 × 1000) / 3600 = 2.5 m/s  
- Speed of policeman = 10 km/h = (10 × 1000) / 3600 ≈ 2.78 m/s

Step 2: Calculate relative speed of policeman with respect to thief.  
- Relative speed = 2.78 - 2.5 = 0.28 m/s

Step 3: Calculate time taken by policeman to catch the thief.  
- Initial distance between them = 200 m  
- Time = Distance / Relative speed = 200 / 0.28 ≈ 714.29 seconds

Step 4: Calculate distance run by thief in this time.  
- Distance = speed × time = 2.5 × 714.29 = 1785.7 m ≈ 1.8 km

Therefore, the thief will have to run approximately 1.8 km before he is overtaken.

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