A thief runs at 8 km/h and a policeman chases at 10 km/h. If the thief has a 100 m head start, how much time will the policeman take to catch him?

Introduction / Context:When two objects move in the same direction, the catching time depends on their relative speed. This is a standard relative speed chase problem with a head start measured in metres that must be converted consistently.

Given Data / Assumptions:

• Thief speed = 8 km/h.
• Policeman speed = 10 km/h.
• Initial gap = 100 m = 0.1 km.

Concept / Approach:Relative speed (closing speed) when both run in the same direction is the difference: 10 - 8 = 2 km/h. Time to catch is gap / relative speed, converted to minutes.

Step-by-Step Solution:

Verification / Alternative check:In 3 min the policeman gains 2 km/h * (3/60) h = 0.1 km, exactly the head start distance.

Why Other Options Are Wrong:2, 4, and 6 min would correspond to gains of 0.0667, 0.1333, and 0.2 km respectively, which do not match the 0.1 km gap.

Common Pitfalls:Failing to convert 100 m to 0.1 km and using sum instead of difference for relative speed in same direction.

Final Answer:3 min