Distance Between a Thief and a Policeman: A Speed and Time Analysis

The problem of determining the distance between a thief and a policeman is one of classic speed and time problems. Let's delve into the calculation with a step-by-step approach.

Problem Statement

A policeman and a thief are separated by 200 meters. The thief starts running at a speed of 10 km/hr, while the policeman runs at a speed of 11 km/hr. We need to determine the distance between them after 6 minutes.

Converting Speeds

Policeman's Speed:
11 km/hr (11 * 1000 m) / (1 hr * 3600 s) ≈ 3.06 m/s

Thief's Speed:
10 km/hr (10 * 1000 m) / (1 hr * 3600 s) ≈ 2.78 m/s

Calculating Distance Traveled in 6 Minutes

The time 6 minutes is equal to:

6 minutes 6 * 60 360 seconds

The distance traveled by the thief in 360 seconds is calculated as:

Distance thief Speed thief * Time 2.78 m/s * 360 s ≈ 1000.8 meters

The distance covered by the policeman in 360 seconds is:

Distance policeman 3.06 m/s * 360 s ≈ 1099 meters

Determining the Relative Distance

The initial distance between the thief and the policeman is 200 meters. After 6 minutes, the distance between them is:

Distance between Initial distance - (Distance thief - Distance policeman) 200 - (1000.8 - 1099) ≈ 101.8 meters

Relative Speed Approach

Alternatively, we can calculate the relative speed:

Relative speed 11 - 10 1 km/hr

Convert this relative speed to meters per second:

1 km/hr (1 * 1000) / (3600) 1/3.6 ≈ 0.28 m/s

In 6 minutes (360 seconds), the relative distance covered is:

0.28 * 360 ≈ 100.8 meters

So, the distance between the thief and the policeman after 6 minutes is:

200 - 100.8 99.2 meters ≈ 100 meters

Conclusion

After 6 minutes, the distance between the policeman and the thief is approximately **101.8 meters**. This problem helps us understand the concept of relative speed and its application in real-world scenarios involving distance and time.

If you're looking for a more visual explanation, you can watch this video guide for a clearer understanding.