Multiple choice

A thief seeing a policeman from a distance of $200$ metres starts running at a speed of $8$ km/hr. The policeman gives chase immediately with a speed of $9$ km/hr and the thief is caught. What is the distance run by the thief?

  1. $1000$ metres
  2. $1200$ metres
  3. $1600$ metres
  4. $2000$ metres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = 9 - 8 = 1 km/hr = 1000/3600 m/s = 5/18 m/s. Time to catch = distance / relative speed = 200 / (5/18) = 720 seconds. Distance run by thief = speed * time = (8 * 1000 / 3600) * 720 = (80/36) * 720 = 80 * 20 = 1600 meters.

AI explanation

Using the relative speed concept for objects moving in the same direction, the relative speed is 9 km/hr minus 8 km/hr, equaling 1 km/hr. The initial gap of 200 metres is 0.2 km, so the time taken to catch the thief is 0.2 km divided by 1 km/hr, which is 0.2 hours. The distance run by the thief is his speed multiplied by this time, or 8 km/hr multiplied by 0.2 hours, resulting in 1.6 km, which equals 1600 metres.

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