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. 4 m/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 the two cars, we can break it down into a series of steps:

### Step 1: Define Variables
Let:
- \( V_A \) = speed of car A (in meters per second)
- \( V_B \) = speed of car B (in meters per second)

### Step 2: Set Up Equations for Opposite Directions
When the two cars are traveling in opposite directions, they get closer by 8 meters every second. This means:
\[ V_A + V_B = 8 \quad \text{(Equation 1)} \]

### Step 3: Set Up Equations for Same Directions
When the two cars are traveling in the same direction, they get closer by 0.8 meters every second. This means:
\[ V_A - V_B = 0.8 \quad \text{(Equation 2)} \]

### Step 4: Solve the Equations
Now we have two equations:
1. \( V_A + V_B = 8 \)
2. \( V_A - V_B = 0.8 \)

We can add these two equations together to eliminate \( V_B \):
\[ (V_A + V_B) + (V_A - V_B) = 8 + 0.8 \]
This simplifies to:
\[ 2V_A = 8.8 \]
Now, divide both sides by 2:
\[ V_A = \frac{8.8}{2} = 4.4 \, \text{m/s} \]

### Step 5: Find the Speed of Car B
Now that we have \( V_A \), we can substitute it back into Equation 1 to find \( V_B \):
\[ 4.4 + V_B = 8 \]
Subtract 4.4 from both sides:
\[ V_B = 8 - 4.4 = 3.6 \, \text{m/s} \]

### Conclusion
The speeds of the two cars are:
- Speed of car A, \( V_A = 4.4 \, \text{m/s} \)
- Speed of car B, \( V_B = 3.6 \, \text{m/s} \)