Multiple choice

A thief is spotted by a policeman from a distance of $100$ metres. When the policeman starts the chase the thief also starts running. If the speed of the thief is $8$ km/hr and that of the policeman $10$ km/hr, how far the thief will have to run before he is overtaken ?

  1. $300$ m
  2. $350$ m
  3. $400$ m
  4. $450$ m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = 10 - 8 = 2 km/hr = 2 * (5/18) m/s = 5/9 m/s. Time to overtake = 100 / (5/9) = 180 seconds. Distance thief runs = 8 km/hr * (180/3600) hr = 8 * (1/20) = 0.4 km = 400 m.

AI explanation

Using the relative speed concept for objects moving in the same direction, the policeman's relative speed to the thief is 10 km/hr minus 8 km/hr, which equals 2 km/hr. The time taken to close the initial gap of 100 metres (or 0.1 km) is distance divided by relative speed: 0.1 km divided by 2 km/hr equals 0.05 hours. In that time, the distance the thief runs is his speed times the time: 8 km/hr multiplied by 0.05 hours gives 0.4 km, which is 400 metres. The result is 400 m.

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