Question

A thief flees city $A$ in a car towards city $B$ on a stretch of straight road, $400$ kilometers long, at a speed of $60$ km/hr. In $30$ minutes a police party leaves city $A$ to chase the thief at $80$ km/hr. Find the distance travelled by the police when it catches thief.

Answer 1

In this question the thief travelled for the first 30 minutes. The speed of thief is 60 km/hr, so he has covered 30 km in 30 minutes.

The ratio of speeds of thief and police is 60: 80 or 3: 4.

Excluding the first 30 minutes, the thief and the police have run for the same time. So the distance covered is in the ratio of their speeds i.e. 3: 4.

Since, the initial distance between the thief and the police if 30 km, so in total, thief and police have covered 90 km and 120 km respectively (to make the ratio 3:4).