Question

A thief sees a jeep at a distance of 250 m, coming towards him at 36 km/h. Thief takes 5 seconds to realise that there is nothing but the police is approaching him by the jeep and start running away from police at 54 km/h. But police realise after 10 seconds when the thief starts running away, that he is actually a thief and gives chase at 72 km/h. How long after thief saw police did police catch up with him and what is the distance police had to travel to do so?

• A. 50 s, 1000 m
• B. 65 s, 1150 m
• C. 65 s, 1300 m
• D. 45 s, 1050 m

Answer 1

The correct option is B 65 s, 1150 m

Initial speed of police = 10 m/s, Increased speed of police = 20 m/s
Speed of thief = 15 m/s
Initial difference between thief and police = 250 m After 5 seconds difference between thief and police $=250-(5\times 10)=200m$
After 10 seconds more, the difference between thief and police $=200+(5\times 10)=250m.$
Now, the time required by police to catch th thief $=\frac{250}{5}=50s$
Distance travelled $=50\times 20=1000m$
Total time = $50+15=65s$
Total distance $=1000+(15\times 10)=1150m$