Type 11: Chasing Problems – Police & Thief
Type 11: Chasing Problems – Police & Thief
Q. A thief is 200 m ahead of a police officer. The thief runs at 10 km/h, while the police officer runs at 12 km/h. In how much time will the police catch the thief ?
Formula:
Time to Catch = Initial Distance ÷ Relative Speed
For the same direction: Relative Speed = Police Speed − Thief Speed
Solution:
Initial distance = 200 m
Police speed = 12 km/h
Thief speed = 10 km/h
Relative speed = 12 − 10 = 2 km/h
Convert into m/s: 2 × 5/18 = 5/9 m/s2
Therefore, Time = 200 / 5/9 = 200 × 9/5 = 360 seconds 360 seconds = 6 minutes
Ans: 360 seconds (6 minutes)
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Practice Set – Police & Thief
Q1. A thief is 300 m ahead of a policeman. The thief runs at 8 km/h, while the policeman runs at 11 km/h. In how much time will the policeman catch the thief ?
A) 4 min B) 5 min C) 6 min D) 8 min
Q2. A thief is 500 m ahead of a policeman. The thief runs at 9 km/h, and the policeman runs at 15 km/h. How long will it take to catch the thief ?
A) 3 min B) 4 min C) 5 min D) 6 min
Q3. A thief is 400 m ahead of a policeman. The thief runs at 10 km/h, while the policeman runs at 14 km/h. Find the catching time.
A) 4 min B) 5 min C) 6 min D) 8 min
Q4. A thief is 600 m ahead of a policeman. The thief runs at 12 km/h, and the policeman runs at 18 km/h. In how much time will the thief be caught ?
A) 4 min B) 5 min C) 6 min D) 8 min
Q5. A thief is 250 m ahead of a policeman. The thief runs at 6 km/h, while the policeman runs at 9 km/h. Find the time taken by the policeman to catch him.
A) 3 min B) 4 min C) 5 min D) 6 min