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