Two cars A and B are running in the same direction. Car ‘A’ had already covered a distance of 60 km. When car ‘B’ started running. The cars meet each other in 3 hours after car ‘B’ started running. What was the speed of Car ‘A’?

Options

A. 40 kmph
B. 60 kmph
C. 45 kmph
D. Cannot be determined

Answer

To solve the problem, we need to determine the speed of Car A based on the information provided.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- Car A has already covered a distance of 60 km before Car B starts moving.
- After Car B starts, they meet after 3 hours.

2. **Distance Covered by Car B**:
- When Car B starts, Car A is already 60 km ahead.
- In the 3 hours that Car B is running, it needs to cover the same distance that Car A has already covered to meet it.
- Therefore, Car B must cover a distance of 60 km to meet Car A.

3. **Calculating the Speed of Car B**:
- Let the speed of Car B be \( v_B \) km/h.
- Since Car B covers 60 km in 3 hours, we can calculate its speed:
\[ v_B = \frac{\text{Distance}}{\text{Time}} = \frac{60 \text{ km}}{3 \text{ hours}} = 20 \text{ km/h} \]

4. **Relative Speed**:
- Since both cars are moving in the same direction, the relative speed of Car A with respect to Car B is:
\[ v_{AB} = v_A - v_B \]
- Where \( v_A \) is the speed of Car A.

5. **Distance Covered by Car A in 3 hours**:
- In the same 3 hours, Car A would have covered additional distance:
\[ \text{Distance covered by Car A} = v_A \times 3 \]

6. **Setting Up the Equation**:
- The total distance covered by Car A when they meet is:
\[ 60 \text{ km} + v_A \times 3 \]
- This distance must equal the distance covered by Car B (60 km):
\[ 60 + 3v_A = 60 + 3v_B \]
- Since we know \( v_B = 20 \text{ km/h} \):
\[ 60 + 3v_A = 60 + 60 \]
- Simplifying gives:
\[ 3v_A = 60 \]
- Therefore, solving for \( v_A \):
\[ v_A = \frac{60}{3} = 20 \text{ km/h} \]

7. **Conclusion**:
- The speed of Car A is 20 km/h.