A policeman notices a thief at a distance of 200 metres and both start running in the same direction, the thief at 10 km/h and the policeman at 11 km/h. What will be the distance between them after 6 minutes?

Introduction / Context:
This problem is a relative speed question involving a chase in one dimension. The policeman and the thief are moving in the same direction with different speeds, and we are asked to find how the gap between them changes after a certain time. Understanding relative speed is crucial for many time and distance and chase problems.

Given Data / Assumptions:

• Initial distance between policeman and thief = 200 metres.
• Speed of thief = 10 km/h.
• Speed of policeman = 11 km/h.
• Both run in the same direction.
• We need the distance between them after 6 minutes.

Concept / Approach:
When two objects move in the same direction, their relative speed is the difference of their speeds. Since the policeman runs faster, he is closing the gap with the thief at a rate equal to (11 - 10) km/h = 1 km/h. We convert time into hours and then compute how much of the initial gap is closed in that time. The remaining distance is the new separation.

Step-by-Step Solution:
Step 1: Relative speed of policeman with respect to thief = 11 - 10 = 1 km/h. Step 2: Convert 6 minutes into hours: 6 minutes = 6 / 60 = 0.1 hour. Step 3: Distance by which the gap reduces in 0.1 hour = Relative speed * Time = 1 * 0.1 = 0.1 km. Step 4: Convert 0.1 km to metres: 0.1 * 1000 = 100 metres. Step 5: Initial gap = 200 metres, so distance between them after 6 minutes = 200 - 100 = 100 metres.
Verification / Alternative check:
We can find actual distances covered in 6 minutes. In 0.1 hour, thief covers 10 * 0.1 = 1 km = 1000 metres. Policeman covers 11 * 0.1 = 1.1 km = 1100 metres. The difference in distances covered in that time is 1100 - 1000 = 100 metres, which matches the computed remaining gap of 100 metres, confirming the answer.

Why Other Options Are Wrong:

• 150 m: This would imply the policeman closed only 50 metres, which contradicts relative speed of 1 km/h over 0.1 hour.
• 190 m: Implies the gap reduced by just 10 metres, clearly incorrect.
• 200 m: Means no change in distance, which is impossible when speeds are different.

Common Pitfalls:

• Adding the speeds instead of subtracting them for motion in the same direction.
• Forgetting to convert minutes into hours before using km/h.
• Interpreting 200 metres as 200 km and making unit errors.

Final Answer:
The distance between the policeman and the thief after 6 minutes is 100 m.