A thief is running away on a straight road in a jeep moving with a speed of 9m/s. A police man chases him on a motor cycle moving at a speed of 10 m/s. If the instantaneous separation of the jeep from the motorcycle is 100m, how long will it take for the police man to catch the thief?

Options

A. 1 s
B. 19 s
C. 90 s
D. 100 s

Answer

To solve the problem of how long it will take for the policeman to catch the thief, we can follow these steps:

### Step 1: Understand the scenario
- The thief is moving away in a jeep at a speed of 9 m/s.
- The policeman is chasing him on a motorcycle at a speed of 10 m/s.
- The initial separation between the jeep and the motorcycle is 100 meters.

### Step 2: Determine the relative speed
- The relative speed of the policeman with respect to the thief can be calculated by subtracting the speed of the thief from the speed of the policeman.

\[ \text{Relative Speed} = \text{Speed of Policeman} - \text{Speed of Thief} = 10 \, \text{m/s} - 9 \, \text{m/s} = 1 \, \text{m/s} \]

### Step 3: Calculate the time to catch up
- To find the time it takes for the policeman to catch the thief, we can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

- Here, the distance is the initial separation of 100 meters, and the relative speed is 1 m/s.

\[ \text{Time} = \frac{100 \, \text{m}}{1 \, \text{m/s}} = 100 \, \text{s} \]

### Conclusion
- Therefore, it will take the policeman 100 seconds to catch the thief.

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