The distance between two cities A and B is 520 km. One car starts from city A towards city B with the speed of 60 km/hr. At the same time, another car starts form city B towards city A with a speed of 70 km/hr. After how many hours they will cross each other?

Options

A. 5 hours
B. 6 hours
C. 3 hours
D. 4 hours

Answer

To solve the problem, we need to determine when the two cars will cross each other as they travel towards each other from cities A and B.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Distance between cities A and B: 520 km
- Speed of car from city A: 60 km/hr
- Speed of car from city B: 70 km/hr

2. **Calculate the Relative Speed:**
Since both cars are moving towards each other, we can find their relative speed by adding their individual speeds.
\[ \text{Relative Speed} = \text{Speed of Car A} + \text{Speed of Car B} = 60 \text{ km/hr} + 70 \text{ km/hr} = 130 \text{ km/hr} \]

3. **Use the Formula for Time:**
The time taken for the two cars to cross each other can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
Substituting the known values:
\[ \text{Time} = \frac{520 \text{ km}}{130 \text{ km/hr}} = 4 \text{ hours} \]

4. **Conclusion:**
The two cars will cross each other after 4 hours.