Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks What is the time (in seconds) which they take to cross each other?

Answer

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

### Step 1: Identify the lengths of the trains
- Train 1 length = 140 meters
- Train 2 length = 160 meters

### Step 2: Calculate the total distance to be covered when the trains cross each other
- Total distance = Length of Train 1 + Length of Train 2
- Total distance = 140 m + 160 m = 300 m

### Step 3: Identify the speeds of the trains
- Speed of Train 1 = 60 km/hr
- Speed of Train 2 = 40 km/hr

### Step 4: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, we add their speeds:
- Relative speed = Speed of Train 1 + Speed of Train 2
- Relative speed = 60 km/hr + 40 km/hr = 100 km/hr

### Step 5: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor (1 km/hr = 5/18 m/s):
- Relative speed in m/s = 100 km/hr × (5/18) = (100 × 5) / 18 = 500 / 18 m/s ≈ 27.78 m/s

### Step 6: Calculate the time taken to cross each other
Using the formula:
- Time = Distance / Speed
- Time = Total distance / Relative speed
- Time = 300 m / (500 / 18) m/s

### Step 7: Simplify the calculation
- Time = 300 m × (18 / 500) = (300 × 18) / 500
- Time = 5400 / 500 = 10.8 seconds

### Final Answer
The time taken for the two trains to cross each other is approximately **10.8 seconds**.

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