Time and Distance – Pursuit and relative speed (policeman chasing thief): A thief runs at 8 km/h and is 100 m ahead of a policeman who runs at 10 km/h. Assuming both maintain their speeds, how long will it take the policeman to catch the thief?

Introduction / Context:
In linear pursuit with both runners on the same line, the catch-up time equals the head start distance divided by the relative speed. Converting the head start to the same units as speeds avoids mistakes.

Given Data / Assumptions:

• Thief speed = 8 km/h.
• Policeman speed = 10 km/h.
• Head start = 100 m = 0.1 km.

Concept / Approach:
Relative speed (closing speed) = 10 − 8 = 2 km/h. Time = gap / relative speed, then convert hours to minutes.

Step-by-Step Solution:
Time (h) = 0.1 / 2 = 0.05 h.Time (min) = 0.05 * 60 = 3 min.

Verification / Alternative check:
In 3 minutes, policeman covers 0.5 km, thief covers 0.4 km, so the 0.1 km head start is exactly closed.

Why Other Options Are Wrong:
2 or 4 minutes correspond to relative speeds of 3 or 1.5 km/h, not present here; 6 minutes doubles the correct value; 90 seconds halves it.

Common Pitfalls:
Failing to convert 100 m to 0.1 km or subtracting speeds in the wrong order.

Final Answer:
3 min