Places A and B are 160 km apart on a highway. One car starts from A and another from B at the same time. If they travel in the same direction, they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.

Answer

To solve the problem, we need to find the speeds of two cars traveling between places A and B, which are 160 km apart. We will denote the speed of the first car as \( x \) km/h and the speed of the second car as \( y \) km/h.

### Step 1: Set up the equations based on the given information.

1. **Same Direction:** When both cars travel in the same direction, they meet after 8 hours. The relative speed when traveling in the same direction is \( x - y \). The distance covered is 160 km.
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ 160 = (x - y) \times 8 \]
Dividing both sides by 8:
\[ x - y = 20 \quad \text{(Equation 1)} \]

2. **Towards Each Other:** When both cars travel towards each other, they meet after 2 hours. The relative speed when traveling towards each other is \( x + y \).
\[ 160 = (x + y) \times 2 \]
Dividing both sides by 2:
\[ x + y = 80 \quad \text{(Equation 2)} \]

### Step 2: Solve the equations.

Now we have a system of two equations:
1. \( x - y = 20 \) (Equation 1)
2. \( x + y = 80 \) (Equation 2)

We can solve these equations simultaneously.

**Adding Equation 1 and Equation 2:**
\[ (x - y) + (x + y) = 20 + 80 \]
\[ 2x = 100 \]
\[ x = 50 \quad \text{(Speed of the first car)} \]

**Substituting \( x \) back into Equation 1 to find \( y \):**
\[ 50 - y = 20 \]
\[ y = 50 - 20 \]
\[ y = 30 \quad \text{(Speed of the second car)} \]

### Conclusion:
The speed of the first car is \( 50 \) km/h, and the speed of the second car is \( 30 \) km/h.