Point 'A' and 'B' are 70 km apart on a highway. A car starts from 'A' and another from 'B' at the same time. If they travel in the same direction they meet in 7 hours, but if they travel towards each other they meet in one hour. Find the speed of the two cars (in km/hr)

Options

A. 20,30
B. 40,30
C. 30,50
D. 20,40

Answer

To solve the problem, we need to find the speeds of two cars that start from points A and B, which are 70 km apart. Let's denote the speed of the car starting from A as \( A \) km/hr and the speed of the car starting from B as \( B \) km/hr.

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

1. **When the cars travel in the same direction:**
- They meet after 7 hours.
- The distance covered by the faster car minus the distance covered by the slower car equals the distance between A and B.
- The equation is:
\[ 70 = (A - B) \times 7 \]
Simplifying this gives:
\[ A - B = 10 \quad \text{(Equation 1)} \]

2. **When the cars travel towards each other:**
- They meet after 1 hour.
- The combined distance they cover equals the distance between A and B.
- The equation is:
\[ 70 = (A + B) \times 1 \]
Simplifying this gives:
\[ A + B = 70 \quad \text{(Equation 2)} \]

### Step 2: Solve the equations.

Now we have two equations:
1. \( A - B = 10 \) (Equation 1)
2. \( A + B = 70 \) (Equation 2)

We can solve these equations simultaneously.

- **Add Equation 1 and Equation 2:**
\[ (A - B) + (A + B) = 10 + 70 \]
This simplifies to:
\[ 2A = 80 \]
Dividing both sides by 2 gives:
\[ A = 40 \quad \text{(Speed of car A)} \]

- **Substitute \( A \) back into Equation 2 to find \( B \):**
\[ 40 + B = 70 \]
Subtracting 40 from both sides gives:
\[ B = 30 \quad \text{(Speed of car B)} \]

### Conclusion:
The speeds of the two cars are:
- Speed of car A = 40 km/hr
- Speed of car B = 30 km/hr