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A thief is spotted by a policeman from a distance of 400 meters. When the policeman started running after the thief, the thief also started running. Assuming the speed of the thief to be 8 km/h and that of the policeman is 10 km/h, how far will the thief have run before he is overtaken by the policeman?

A thief is spotted by a policeman from a distance of 400 meters. When the policeman started running after the thief, the thief also started running. Assuming the speed of the thief to be 8 km/h and that of the policeman is 10 km/h, how far will the thief have run before he is overtaken by the policeman? Correct Answer 1600 meters

Given: Distance between the policeman and thief = 400 meters

Speed of the thief = 8 km/h

Speed of the policeman = 10 km/h

Formula used:

Speed = Distance/Time

Concept used:

Relative speed = Speed of policeman – Speed of thief

Calculation:

Relative speed = 10 – 8

⇒ 2 km/h

Or 2× (5/18)

⇒ 5/9 m/s

Time taken by policeman to overtake the thief = 400/(5/9)

⇒ (400 × 9)/5

⇒ 80 × 9

⇒ 720 seconds

Distance covered by the thief = 720 × 8 × (5/18)

⇒ 40 × 8 × 5

∴ 1600 meters

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