Two trains one 160 m and the other 140 m long are running in opposite directions on parallel rails, the first at 77 km an hour and the other at 67 km an hour. How long will they take to cross each other?

Options

A. 7 seconds
B. `7 (1)/(2)` seconds
C. 6 seconds
D. 10 seconds

Answer

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

### Step 1: Identify the lengths of the trains
- Train 1 (T1) is 160 meters long.
- Train 2 (T2) is 140 meters long.

### Step 2: Identify the speeds of the trains
- Speed of Train 1 (T1) = 77 km/h
- Speed of Train 2 (T2) = 67 km/h

### Step 3: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, we add their speeds:
- Relative Speed = Speed of T1 + Speed of T2
- Relative Speed = 77 km/h + 67 km/h = 144 km/h

### Step 4: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we use the conversion factor (1 km/h = 5/18 m/s):
- Relative Speed in m/s = 144 km/h × (5/18)
- Relative Speed in m/s = 144 × 5 / 18 = 40 m/s

### Step 5: Calculate the total distance to be covered when the trains cross each other
The total distance is the sum of the lengths of both trains:
- Total Distance = Length of T1 + Length of T2
- Total Distance = 160 m + 140 m = 300 m

### Step 6: Calculate the time taken to cross each other
Using the formula for time:
- Time = Distance / Speed
- Time = Total Distance / Relative Speed
- Time = 300 m / 40 m/s = 7.5 seconds

### Final Answer
The two trains will take **7.5 seconds** to cross each other.

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