Distance between A & B is 120 km. If they both move towards each other (opposite direction) they meet in 2 hours but if they move in same direction they meet in 6 hours. Find their speed.

Answer

To solve the problem, we need to determine the speeds of A and B based on the information provided about their meeting times in different directions.

### Step-by-Step Solution:

1. **Understand the Problem:**
- Distance between A and B = 120 km.
- They meet in 2 hours when moving towards each other.
- They meet in 6 hours when moving in the same direction.

2. **Set Up Equations:**
- Let the speed of A be \( x \) km/h and the speed of B be \( y \) km/h.

3. **Equation for Meeting in Opposite Directions:**
- When moving towards each other, their relative speed is \( x + y \).
- They meet in 2 hours, so:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ 120 = (x + y) \times 2 \]
Dividing both sides by 2:
\[ x + y = 60 \quad \text{(Equation 1)} \]

4. **Equation for Meeting in the Same Direction:**
- When moving in the same direction, their relative speed is \( x - y \).
- They meet in 6 hours, so:
\[ 120 = (x - y) \times 6 \]
Dividing both sides by 6:
\[ x - y = 20 \quad \text{(Equation 2)} \]

5. **Solve the Equations:**
- Now we have two equations:
1. \( x + y = 60 \)
2. \( x - y = 20 \)

- Add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 60 + 20 \]
\[ 2x = 80 \]
\[ x = 40 \quad \text{(Speed of A)} \]

- Substitute \( x = 40 \) into Equation 1:
\[ 40 + y = 60 \]
\[ y = 20 \quad \text{(Speed of B)} \]

6. **Final Speeds:**
- Speed of A = 40 km/h
- Speed of B = 20 km/h

### Summary:
- The speed of A is 40 km/h.
- The speed of B is 20 km/h.