Two trains of length 150 m and 300 m long are going parallel in opposite direction at a speed of 90 m/min and 60 m/min respectively. What is the time taken for the trains to cross each other completely ?

Options

A. 1 minute
B. 5 minutes
C. 3 minutes
D. 2 minutes

Answer

To solve the problem of how long it takes for two trains to completely cross each other, we can break it down into a series of steps:

### Step 1: Identify the lengths of the trains
- Train 1 length = 150 meters
- Train 2 length = 300 meters

### Step 2: Calculate the total distance to be covered
When two trains cross each other completely, the distance they need to cover is the sum of their lengths.
- Total distance = Length of Train 1 + Length of Train 2
- Total distance = 150 m + 300 m = 450 meters

### Step 3: Identify the speeds of the trains
- Speed of Train 1 = 90 meters/minute
- Speed of Train 2 = 60 meters/minute

### Step 4: Calculate the relative speed
Since the trains are moving in opposite directions, their speeds will be added to find the relative speed.
- Relative speed = Speed of Train 1 + Speed of Train 2
- Relative speed = 90 m/min + 60 m/min = 150 m/min

### Step 5: Use the formula for time
The time taken to cross each other can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

### Step 6: Substitute the values into the formula
- Time = Total distance / Relative speed
- Time = 450 m / 150 m/min

### Step 7: Calculate the time
- Time = 3 minutes

### Final Answer
The time taken for the trains to cross each other completely is **3 minutes**.

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