A thief is spotted by a policeman from a distance of 200 m. When the policeman starts chasing, the thief also starts running. If the speed of the thief be16km/h and that of the policeman be 20km/h, how far the thief will have run before he is overtaken?

Options

A. 800 m
B. 850 m
C. 700 m
D. 650 m

Answer

To solve the problem, we will follow these steps:

### Step 1: Convert the speeds from km/h to m/s
The speeds of the thief and the policeman are given in kilometers per hour (km/h). We need to convert these speeds to meters per second (m/s) for easier calculations.

- Speed of the thief = 16 km/h
- Speed of the policeman = 20 km/h

To convert km/h to m/s, we use the conversion factor:
1 km/h = (1000 m / 1 km) / (3600 s / 1 h) = 1/3.6 m/s.

Calculating the speeds:
- Speed of the thief in m/s = 16 km/h × (1/3.6) = 4.44 m/s (approximately).
- Speed of the policeman in m/s = 20 km/h × (1/3.6) = 5.56 m/s (approximately).

### Step 2: Determine the relative speed
The relative speed is the difference in speed between the policeman and the thief since they are moving in the same direction.

Relative speed = Speed of policeman - Speed of thief
= 5.56 m/s - 4.44 m/s
= 1.12 m/s.

### Step 3: Calculate the time taken to catch the thief
The policeman starts 200 meters behind the thief. To find out how long it will take for the policeman to catch the thief, we can use the formula:

Time = Distance / Relative Speed.

Substituting the values:
Time = 200 m / 1.12 m/s ≈ 178.57 seconds.

### Step 4: Calculate the distance run by the thief
Now that we have the time taken for the policeman to catch the thief, we can calculate how far the thief has run during this time.

Distance = Speed of thief × Time.
Substituting the values:
Distance = 4.44 m/s × 178.57 s ≈ 792.67 meters.

### Final Answer
The thief will have run approximately 792.67 meters before he is overtaken by the policeman.

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