Q: A police officer spots a thief from 100 metres away. When the cop begins the pursuit, the thief flees as well. If the burglar's speed is 8 km/hr and the policeman's speed is 10 km/hr, how far will the thief have to go before being overtaken?  

The relative speed of the policeman and the thief is given as the speed of the policeman minus the speed of the thief, or 2 km/hr.

The distance between the thief and the policeman is given as 100 meters.

We can use the relative speed to calculate the time it will take for the policeman to catch up to the thief. Since the relative speed is 2 km/hr and the distance between the thief and the policeman is 100 meters, 

the time it will take for the policeman to catch up to the thief is 

100 meters / (2 km/hr * 1000 meters/km) = 1/20 hr.

To find the distance the thief will have run in 1/20 hr at a speed of 8 km/hr, we can use the formula for distance traveled, which is distance = speed * time. 

Plugging in the values given in the problem, we get distance = 8 km/hr * 1/20 hr = 2/5 km = 400 meters.

Therefore, the thief will have run a distance of 400 meters before being overtaken by the policeman.