Two trains 130 m and 110 m in length are running towards each other on parallel tracks, one at the rate of 32 km/h and another at 40 km/h. In what time will they be clear each other from the moment they meet?

Options

A. 5s
B. 25s
C. 10s
D. 12s

Answer

To solve the problem step by step, we need to determine how long it will take for the two trains to completely clear each other after they meet. Here’s how we can do that:

### Step 1: Calculate the total distance to be covered
The total distance that needs to be covered for the two trains to completely clear each other is the sum of their lengths.

- Length of Train 1 = 130 meters
- Length of Train 2 = 110 meters

**Total Distance = Length of Train 1 + Length of Train 2**
Total Distance = 130 m + 110 m = 240 m

### Step 2: Calculate the relative speed of the trains
Since the trains are moving towards each other, we need to add their speeds to find the relative speed.

- Speed of Train 1 = 32 km/h
- Speed of Train 2 = 40 km/h

**Relative Speed = Speed of Train 1 + Speed of Train 2**
Relative Speed = 32 km/h + 40 km/h = 72 km/h

### Step 3: Convert the relative speed from km/h to m/s
To convert the speed from kilometers per hour to meters per second, we use the conversion factor \( \frac{5}{18} \).

**Relative Speed in m/s = Relative Speed in km/h × \( \frac{5}{18} \)**
Relative Speed in m/s = 72 km/h × \( \frac{5}{18} \) = 20 m/s

### Step 4: Calculate the time taken to clear each other
Now, we can use the formula for time, which is given by:

**Time = Distance / Speed**

Substituting the values we have:

**Time = Total Distance / Relative Speed**
Time = 240 m / 20 m/s = 12 seconds

### Final Answer
The time taken for the two trains to completely clear each other after they meet is **12 seconds**.

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