Two cars get closer by 8 m every second while traveling in the opposite directions. They get closer by 0.8 m while traveling in the same directions. What are the speeds of the two cars ?

Options

A. 4m/s and `4.4` m/s
B. `4.4` m/s and `3.6` m/s
C. 4 m/s and `3.6` m/s
D. 4 m/s and 3 m/s

Answer

To solve the problem of finding the speeds of two cars based on their relative motion, we can set up equations based on the information provided.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( V_A \) be the speed of Car A and \( V_B \) be the speed of Car B.

2. **Set Up Equations:**
- When the cars are traveling in opposite directions, they get closer by 8 m every second. This can be expressed as:
\[ V_A + V_B = 8 \quad \text{(Equation 1)} \]
- When the cars are traveling in the same direction, they get closer by 0.8 m every second. This can be expressed as:
\[ V_A - V_B = 0.8 \quad \text{(Equation 2)} \]

3. **Solve the Equations:**
- We can add Equation 1 and Equation 2 to eliminate \( V_B \):
\[ (V_A + V_B) + (V_A - V_B) = 8 + 0.8 \]
This simplifies to:
\[ 2V_A = 8.8 \]
Therefore,
\[ V_A = \frac{8.8}{2} = 4.4 \text{ m/s} \]

- Next, we can substitute \( V_A \) back into Equation 1 to find \( V_B \):
\[ 4.4 + V_B = 8 \]
Rearranging gives:
\[ V_B = 8 - 4.4 = 3.6 \text{ m/s} \]

4. **Final Speeds:**
- The speed of Car A (\( V_A \)) is 4.4 m/s.
- The speed of Car B (\( V_B \)) is 3.6 m/s.

### Summary of Results:
- \( V_A = 4.4 \text{ m/s} \)
- \( V_B = 3.6 \text{ m/s} \)