A police car is ordered to chase a speeding car that is 10 km ahead. The car is travelling at an average speed of 40 km/h and the police car pursues it at an average speed of 50 km/h. How long does it take for the police car to overtake the other car?

Options

A. 60 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 = 40 km/h
- Speed of the police car = 50 km/h

### Step 2: Determine the distance between the two cars
- The speeding car is 10 km ahead of the police car.

### Step 3: Calculate the relative speed
- The relative speed is the difference in speeds between the police car and the speeding car.
- Relative speed = Speed of police car - Speed of speeding car
- Relative speed = 50 km/h - 40 km/h = 10 km/h

### Step 4: Calculate the time taken to close the gap
- To find the time taken for the police car to overtake the speeding car, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
- Here, the distance is 10 km (the initial gap) and the relative speed is 10 km/h.
- Time = \(\frac{10 \text{ km}}{10 \text{ km/h}} = 1 \text{ hour}\)

### Conclusion
- It takes the police car 1 hour to overtake the speeding car.

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