A thief steals an item and escapes, running at 13.5 km/h. A policeman arrives at the spot of the crime after 8 minutes and immediately starts chasing the thief. 28 minutes after the policeman started to chase the thief, there is still a gap of 540 m between the two. At what distance from the spot of the crime would the policeman catch up with the thief, and what is the speed (in km/h) at which the policeman ran?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 10.8 km, 16.2.
Thief's head start = 1.8 km
After 28 min, gap = 0.54 km → Policeman ran 7.56 km
Speed = (7.56 × 60) / 28 = 16.2 km/h
Relative speed = 2.7 km/h → Time to catch = 1.8 / 2.7 = 2/3 hr
Distance = 13.5 × 2/3 + 1.8 = 10.8 km
Speed = 16.2 km/h, Distance = 10.8 km