Two cars move uniformly towards each othar, the distance between them decreases at the rate 50 m/s. If they move in same direction with different speeds, the distance between them increases at the rate 10 m/s. The speed of two cars will be

Options

A. 30 m/s and 20 m/s
B. 40 m/s and 10 m/s
C. 15 m/s and 35 m/s
D. 25 m/s and 25 m/s

Answer

To solve the problem, we will analyze the two scenarios involving the two cars and set up equations based on their relative velocities.

### Step-by-Step Solution:

1. **Understanding the First Scenario:**
- When the two cars are moving towards each other, the distance between them decreases at a rate of 50 m/s.
- Let the speed of car A be \( V_A \) and the speed of car B be \( V_B \).
- The relative velocity when they approach each other is given by:
\[ V_A + V_B = 50 \quad \text{(Equation 1)} \]

2. **Understanding the Second Scenario:**
- When the two cars are moving in the same direction, the distance between them increases at a rate of 10 m/s.
- In this case, the relative velocity is given by:
\[ V_A - V_B = 10 \quad \text{(Equation 2)} \]

3. **Solving the Equations:**
- We have two equations:
- From Equation 1: \( V_A + V_B = 50 \)
- From Equation 2: \( V_A - V_B = 10 \)
- We can add these two equations to eliminate \( V_B \):
\[ (V_A + V_B) + (V_A - V_B) = 50 + 10 \]
\[ 2V_A = 60 \]
\[ V_A = 30 \text{ m/s} \]

4. **Finding the Speed of Car B:**
- Now that we have \( V_A \), we can substitute it back into Equation 1 to find \( V_B \):
\[ 30 + V_B = 50 \]
\[ V_B = 50 - 30 = 20 \text{ m/s} \]

5. **Conclusion:**
- The speeds of the two cars are:
- Speed of car A, \( V_A = 30 \text{ m/s} \)
- Speed of car B, \( V_B = 20 \text{ m/s} \)

### Final Answer:
- The speed of the two cars are \( V_A = 30 \text{ m/s} \) and \( V_B = 20 \text{ m/s} \).