A police car is ordered to chase a speeding car that is 5 km ahead. The car is travelling at an average speed of 80 km/h and the police car pursues it at an average speed of 100 km/h. How long does it take for the police car to overtake the other car?

Options

A. 15 min
B. 16 min
C. 17 min
D. 20 min

Answer

To solve the problem of how long it takes for the police car to overtake the speeding car, we can follow these steps:

### Step 1: Identify the speeds of both cars
- Speed of the speeding car = 80 km/h
- Speed of the police car = 100 km/h

### Step 2: Determine the relative speed
The relative speed is the difference in speed between the police car and the speeding car.
- Relative speed = Speed of police car - Speed of speeding car
- Relative speed = 100 km/h - 80 km/h = 20 km/h

### Step 3: Calculate the distance to cover
The police car needs to cover the initial distance of 5 km that the speeding car is ahead.

### Step 4: Use the formula for time
Time taken to cover a distance can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance is 5 km and the relative speed is 20 km/h.

### Step 5: Substitute the values into the formula
\[ \text{Time} = \frac{5 \text{ km}}{20 \text{ km/h}} \]

### Step 6: Calculate the time
\[ \text{Time} = \frac{5}{20} = 0.25 \text{ hours} \]

### Step 7: Convert hours into minutes
Since 1 hour = 60 minutes,
\[ 0.25 \text{ hours} = 0.25 \times 60 \text{ minutes} = 15 \text{ minutes} \]

### Conclusion
It takes the police car 15 minutes to overtake the speeding car.

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