Two cars started simultaneously towards each other from town A and B that are 480 km apart. It took the first car travelling from A to B 8 hours to cover the distance and the second car travelling from B to A 12 hours. Determine at what distance from A the two cars meet?

Options

A. 288 km
B. 200 km
C. 300 km
D. 196 km

Answer

To find the distance from town A where the two cars meet, we can follow these steps:

### Step 1: Calculate the speeds of both cars.
- The first car travels from A to B and takes 8 hours to cover 480 km.
- The speed of the first car (v1) can be calculated using the formula:

\[ v1 = \frac{\text{Distance}}{\text{Time}} = \frac{480 \text{ km}}{8 \text{ hours}} = 60 \text{ km/h} \]

- The second car travels from B to A and takes 12 hours to cover the same distance.
- The speed of the second car (v2) can be calculated as:

\[ v2 = \frac{\text{Distance}}{\text{Time}} = \frac{480 \text{ km}}{12 \text{ hours}} = 40 \text{ km/h} \]

### Step 2: Determine the time taken until they meet.
Let \( t \) be the time in hours until the two cars meet. During this time, both cars are moving towards each other.

- The distance covered by the first car in time \( t \) is \( v1 \cdot t = 60t \).
- The distance covered by the second car in time \( t \) is \( v2 \cdot t = 40t \).

Since the total distance between A and B is 480 km, we can set up the equation:

\[ 60t + 40t = 480 \]

### Step 3: Solve for \( t \).
Combine the terms:

\[ 100t = 480 \]

Now, divide both sides by 100:

\[ t = \frac{480}{100} = 4.8 \text{ hours} \]

### Step 4: Calculate the distance from A where they meet.
Now that we have the time \( t \), we can find the distance from A to the meeting point:

\[ \text{Distance from A} = v1 \cdot t = 60 \cdot 4.8 = 288 \text{ km} \]

### Conclusion:
The two cars meet at a distance of **288 km from town A**.

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