In a double track rail route, two trains start simultaneously from the opposite stations, 200km apart. The train A runs westwards at a speed of 50 kmph and the opposite train B runs eastwards at 40 kmph. After 3 hours, what will be the distance between these two trains?

Options

A. 30 kms
B. 50 kms
C. 80 kms
D. 70 kms

Explanation

To solve the problem step by step, we can follow these calculations:

### Step 1: Identify the speeds of the trains
- Train A runs westwards at a speed of 50 km/h.
- Train B runs eastwards at a speed of 40 km/h.

### Step 2: Calculate the distance each train travels in 3 hours
- **Distance traveled by Train A**:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 50 \, \text{km/h} \times 3 \, \text{h} = 150 \, \text{km} \]

- **Distance traveled by Train B**:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 40 \, \text{km/h} \times 3 \, \text{h} = 120 \, \text{km} \]

### Step 3: Calculate the total distance traveled by both trains
- The total distance traveled by both trains after 3 hours is:
\[ \text{Total distance} = \text{Distance by Train A} + \text{Distance by Train B} = 150 \, \text{km} + 120 \, \text{km} = 270 \, \text{km} \]

### Step 4: Calculate the remaining distance between the trains
- Initially, the distance between the two trains was 200 km. After 3 hours, they have traveled a total of 270 km towards each other. Therefore, the distance between them is:
\[ \text{Remaining distance} = \text{Initial distance} - \text{Total distance traveled} = 200 \, \text{km} - 270 \, \text{km} \]
Since the total distance traveled is greater than the initial distance, they have crossed each other. The distance between them is:
\[ \text{Distance between trains} = 270 \, \text{km} - 200 \, \text{km} = 70 \, \text{km} \]

### Final Answer:
The distance between the two trains after 3 hours is **70 km**.

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