Multiple choice

A thief is spotted by a policeman from a distance of 350 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief to be 7 km/h and that of the policeman to be 12 km/h, how far would the thief have run before he is overtaken?

  1. 490 metres

  2. 392 metres

  3. 588 metres

  4. 294 metres
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A Correct answer
Explanation

Relative speed = 12 - 7 = 5 km/h = 5 * 5/18 m/s = 25/18 m/s. Time to overtake = Distance / Relative speed = 350 / (25/18) = 350 * 18 / 25 = 14 * 18 = 252 seconds. Distance run by thief = Speed of thief * Time = 7 * (5/18) * 252 = 7 * 5 * 14 = 490 metres.

AI explanation

The relative speed of the policeman and the thief is 12 km/h minus 7 km/h, which equals 5 km/h, and converting this to meters per second gives 25/18 m/s. The policeman must close a gap of 350 meters, so the time taken is 350 divided by 25/18, which equals 252 seconds. The thief runs at 7 km/h, which is 35/18 m/s, so the distance the thief covers is 35/18 multiplied by 252, yielding 490 meters.

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