Two trains are approaching each other on the same track with velocity 100 km/h and 50 km/h. When they are at a distance of 300 km from each other, a bird starts flying from train 1 towards train 2. When the bird reaches train 2, it instantly reverses its direction and flies again towards train 1. This process continues till the bird is trapped between the trains when they collide. If the bird always travels at a constant speed 200 km/h, the total distance the bird flies is:

Options

A. 200 km
B. 400 km
C. 300 km
D. 600 km

Explanation

To solve the problem, we need to determine the total distance the bird flies before the two trains collide. Here’s a step-by-step breakdown of the solution:

### Step 1: Determine the relative velocity of the trains
The two trains are moving towards each other. The velocities of the trains are:
- Train 1: 100 km/h
- Train 2: 50 km/h

To find the relative velocity, we add the speeds of both trains:
\[ \text{Relative Velocity} = 100 \text{ km/h} + 50 \text{ km/h} = 150 \text{ km/h} \]

**Hint:** When two objects move towards each other, their speeds add up to give the relative speed.

### Step 2: Calculate the time until the trains collide
The initial distance between the two trains is 300 km. We can calculate the time until they collide using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Velocity}} \]
Substituting the values:
\[ \text{Time} = \frac{300 \text{ km}}{150 \text{ km/h}} = 2 \text{ hours} \]

**Hint:** To find the time until two moving objects collide, divide the distance by their combined speed.

### Step 3: Calculate the distance the bird flies
The bird flies at a constant speed of 200 km/h. To find the total distance the bird travels during the time until the trains collide, we use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the values:
\[ \text{Distance} = 200 \text{ km/h} \times 2 \text{ hours} = 400 \text{ km} \]

**Hint:** The distance traveled by an object is the product of its speed and the time it travels.

### Final Answer
The total distance the bird flies before the trains collide is **400 km**.