Two trains, one 160m and the other 140m long are running in opposite directions on parallel rails, the first at 77km an hour and the other at 67km 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 the two trains to cross each other, we can follow these steps:

### Step 1: Calculate the total distance to be covered.
The total distance when two trains cross each other is the sum of their lengths.

- Length of the first train = 160 meters
- Length of the second train = 140 meters

**Total Distance (D)** = Length of first train + Length of second train
**D** = 160 m + 140 m = 300 m

### Step 2: Calculate the combined speed of the two trains.
Since the trains are moving in opposite directions, we can add their speeds to get the relative speed.

- Speed of the first train = 77 km/h
- Speed of the second train = 67 km/h

**Combined Speed (S)** = Speed of first train + Speed of second train
**S** = 77 km/h + 67 km/h = 144 km/h

### Step 3: Convert the speed from km/h to m/s.
To convert km/h to m/s, we can use the conversion factor (1 km/h = 5/18 m/s).

**S in m/s** = 144 km/h × (5/18)
**S in m/s** = 144 × 5 / 18 = 40 m/s

### Step 4: Calculate the time taken to cross each other.
Using the formula for time, which is:

**Time (T)** = Total Distance / Combined Speed

**T** = 300 m / 40 m/s
**T** = 7.5 seconds

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

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