Car A is traveling at a speed of 54 km/h on a road. Car B is 100 meters behind Car A, traveling in the same direction as Car A. Car C is traveling along the same road towards Car A in the opposite direction at a speed of 72 km/h and is 280 meters away from Car A. At what speed (in km/h) should Car B travel so that all three cars meet at the same time? 
1) 95.4 
2) 99
3)101
4)106.2

We are given the following details:

- Car A is traveling at 54 km/h.
- Car B is 100 meters behind Car A, traveling in the same direction as Car A.
- Car C is 280 meters ahead of Car A, traveling towards Car A at 72 km/h.

We need to find the speed of Car B such that all three cars meet at the same time.

### Step-by-step solution:

1. **Convert distances to kilometers**: 
   - Car B is 100 meters behind Car A: \( 100 \, \text{m} = 0.1 \, \text{km} \)
   - Car C is 280 meters away from Car A: \( 280 \, \text{m} = 0.28 \, \text{km} \)

2. **Determine the time for Cars A and C to meet**:
   The relative speed of Cars A and C is the sum of their speeds because they are moving towards each other:
   \[
   \text{Relative speed} = 54 \, \text{km/h} + 72 \, \text{km/h} = 126 \, \text{km/h}
   \]
   The time taken for Cars A and C to meet is:
   \[
   \text{Time} = \frac{\text{Distance between A and C}}{\text{Relative speed}} = \frac{0.28 \, \text{km}}{126 \, \text{km/h}} = \frac{0.28}{126} \approx 0.00222 \, \text{hours}
   \]
   This is equivalent to \( 0.00222 \times 60 = 0.133 \, \text{minutes} \), or roughly 8 seconds.

3. **Determine the speed of Car B**:
   Car B needs to cover the distance between itself and Car A (which is 0.1 km) in the same time (0.00222 hours) to meet Car A and Car C simultaneously. Let \( v_B \) be the speed of Car B. The time it takes Car B to meet Car A is:
   \[
   \text{Time} = \frac{0.1 \, \text{km}}{v_B} = 0.00222 \, \text{hours}
   \]
   Solving for \( v_B \):
   \[
   v_B = \frac{0.1}{0.00222} \approx 45 \, \text{km/h}
   \]
   However, Car B is already traveling at the same speed as Car A, meaning it doesn't need to catch up to Car A in this particular scenario. Therefore, its speed for matching

Car A is traveling at a speed of 54 km/h on a road. Car B is 100 meters behind Car A, traveling in the same direction as Car A. Car C is traveling along the same road towards Car A in the opposite direction at a speed of 72 km/h and is 280 meters away from Car A. At what speed (in km/h) should Car B travel so that all three cars meet at the same time?

Discover how to solve a relative speed problem where three cars on the same road need to meet simultaneously. With Car A at 54 km/h, Car B at an unknown speed, and Car C approaching at 72 km/h from 280 meters away, this problem uses key algebraic concepts and formulas, ideal for students in Grades 10-12.

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