You are driving from point A to point B at a speed of 45 km-'hr. Your hi end is driving from point B to point A at a speed 3 of 53 km/hr. If the distance between the two points is 1029 km and both of you started at the same time, how many hours will it be before you pass each other ?
A)`9.5`
B)10
C)11
D)10.5

Options

A. `9.5`
B. 10
C. 11
D. `10.5`

Answer

To solve the problem, we need to determine how long it will take for two vehicles traveling towards each other to meet.

### Step-by-Step Solution:

1. **Identify the Speeds and Distance**:
- Speed of the first vehicle (from A to B): \(45 \text{ km/hr}\)
- Speed of the second vehicle (from B to A): \(53 \text{ km/hr}\)
- Distance between points A and B: \(1029 \text{ km}\)

2. **Calculate the Relative Speed**:
- Since both vehicles are moving towards each other, we add their speeds to find the relative speed.
\[ \text{Relative Speed} = 45 \text{ km/hr} + 53 \text{ km/hr} = 98 \text{ km/hr} \]

3. **Use the Formula for Time**:
- The formula to calculate time when distance and speed are known is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Here, the distance is \(1029 \text{ km}\) and the relative speed is \(98 \text{ km/hr}\).
\[ \text{Time} = \frac{1029 \text{ km}}{98 \text{ km/hr}} \]

4. **Perform the Division**:
- To find the time, we divide \(1029\) by \(98\):
\[ 1029 \div 98 \approx 10.5 \text{ hours} \]

5. **Conclusion**:
- Therefore, the time before the two vehicles pass each other is approximately \(10.5\) hours.

### Answer:
The correct answer is **D) 10.5 hours**.

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