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A policeman spots the thief at a distance of 100 m running away at a speed of 12 km/h. The policeman waits for 1 minute and then starts chasing the thief at a speed of 16 km/h. How much time will be taken by the policeman to catch the thief?

A policeman spots the thief at a distance of 100 m running away at a speed of 12 km/h. The policeman waits for 1 minute and then starts chasing the thief at a speed of 16 km/h. How much time will be taken by the policeman to catch the thief? Correct Answer 4.5 minutes

GIVEN:

Policeman spots the thief at a distance of 100 m running away at a speed of 12 km/h.

Speed of Policeman = 16 km/h

CONCEPT:

Relative speed.

Unit Conversion, To convert km/hr to m/s, we need to multiply by 5/18.

12 km/h = 12 × 5/18 = 10/3 m/s

16 km/h = 16 × 5/18 = 40/9 m/s

CALCULATION:

Since the thief has a head-start of 100 metres, and also 1 minute ( = 60 seconds)

⇒ Distance covered by the thief before the policeman starts chasing = 10/3 × 60

⇒ Distance covered = 200 metres

⇒ The thief has a head start of 300 meters ( = 100 + 200).

⇒ the relative speed = 40/9 – 10/3

⇒ the relative speed = 10/9 m/s

⇒ Time taken by the policeman to catch the thief = 300/(10/9)

⇒ Time taken by the policeman to catch the thief = 270 seconds (or 4.5 minutes)

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