Two trains of length 140m and 100m long are going on a parallel track in same direction at a speed of 90 km/ph and 18 km/ph respectively. What is the time taken for the trains to cross each other completely?

Options

A. 12 seconds
B. 13 seconds
C. 15 seconds
D. 14 seconds

Answer

To solve the problem of how long it takes for two trains to completely cross each other, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Length of Train A = 140 m
- Length of Train B = 100 m

### Step 2: Calculate the total distance to be covered when the trains cross each other
- Total distance = Length of Train A + Length of Train B
- Total distance = 140 m + 100 m = 240 m

### Step 3: Determine the speeds of the trains
- Speed of Train A = 90 km/h
- Speed of Train B = 18 km/h

### Step 4: Calculate the relative speed of the trains
Since the trains are moving in the same direction, the relative speed is calculated by subtracting the speed of the slower train from the speed of the faster train.
- Relative speed = Speed of Train A - Speed of Train B
- Relative speed = 90 km/h - 18 km/h = 72 km/h

### Step 5: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).
- Relative speed in m/s = 72 km/h × \( \frac{5}{18} \)
- Relative speed in m/s = 20 m/s

### Step 6: Calculate the time taken to cross each other
Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Time = \( \frac{240 \text{ m}}{20 \text{ m/s}} \)
- Time = 12 seconds

### Conclusion
The time taken for the trains to cross each other completely is **12 seconds**.

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