A policeman spots a thief from a distance of 100 metres. When he starts running after the thief, the thief starts running as well. How far will the thief have to run before being overtaken if his speed is 8 km/h and the policeman's speed is 10 km/h?

Given:

Distance between the policeman and the thief = 100 metres

Speed of the thief = 8 km/h

Speed of the policeman = 10 km/h

Calculation:

Relative speed between the policeman and the thief:

Relative speed = Policeman's speed - Thief's speed

Relative speed = 10 km/h - 8 km/h = 2 km/h

Convert the relative speed to metres per second:

1 km/h = 1000 metres / 3600 seconds

Relative speed = 2 km/h = (2 × 1000) / 3600 = 5/9 metres per second

Calculate the time taken by the policeman to catch the thief:

The policeman has to cover the 100 metres gap.

Time = Distance / Relative speed

Time = 100 / (5/9) = 100 × 9 / 5 = 180 seconds

Distance run by the thief in 180 seconds:

Speed of the thief = 8 km/h = (8 × 1000) / 3600 = 20/9 metres per second

Distance run by the thief = Speed × Time = (20/9) × 180 = 400 metres

∴ The thief will have to run 400 metres before being overtaken by the policeman.