A thief takes off on his bike at a certain speed after seeing a police car at a distance of 250 m. The police car starts chasing…

Question

A thief takes off on his bike at a certain speed after seeing a police car at a distance of 250 m. The police car starts chasing and catches him. If the thief runs 1.5 km before being caught and the speed of the police car is 70 km/h, then what is the speed of the thief's bike (in km/h)?

1. A. 65
2. B. 50
3. C. 55
4. D. 60 (Correct answer)

Correct Answer

Option D — 60

Detailed Solution & Explanation

The correct answer is 60.

Key Points

• In the same time, the police car covers $1.5\text{ km}+250\text{ m}=1.75$ km while the thief covers 1.5 km.
• Equal time: $\dfrac{1.75}{70}=\dfrac{1.5}{v}\Rightarrow v=\dfrac{1.5\times70}{1.75}=60$ km/h.

Additional Information

• Chase problems are solved on equal time: whatever the speeds, both cover their distances in the same interval, so distance ÷ speed is equal for the two.
• The head start is added to the pursuer's distance, not subtracted from the runner's — 1.5 km + 250 m = 1.75 km.
• Keep units consistent before dividing; mixing metres with kilometres is the usual source of error here.