Two trains each of length 100 m moving parallel towards each other at speed 72km/h and 36km/h respectively. In how much time will they cross each other?

Options

A. 4.5 s
B. 6.67 s
C. 3.5 s
D. 7.25 s

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: Convert the speeds from km/h to m/s
The speeds of the trains are given in kilometers per hour (km/h). We need to convert these speeds to meters per second (m/s) for our calculations.

- Speed of Train 1 (v1) = 72 km/h
- Speed of Train 2 (v2) = 36 km/h

To convert km/h to m/s, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

Calculating the speeds:
- \( v1 = 72 \times \frac{5}{18} = 20 \text{ m/s} \)
- \( v2 = 36 \times \frac{5}{18} = 10 \text{ m/s} \)

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

\[ \text{Relative speed (v)} = v1 + v2 = 20 \text{ m/s} + 10 \text{ m/s} = 30 \text{ m/s} \]

### Step 3: Calculate the total distance to be covered
Each train has a length of 100 m. Therefore, the total distance that needs to be covered when the two trains cross each other is the sum of their lengths.

\[ \text{Total distance} = \text{Length of Train 1} + \text{Length of Train 2} = 100 \text{ m} + 100 \text{ m} = 200 \text{ m} \]

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

\[ \text{Time (t)} = \frac{\text{Distance}}{\text{Speed}} \]

We can now substitute the values we have calculated:

\[ t = \frac{200 \text{ m}}{30 \text{ m/s}} \]

Calculating the time:

\[ t = \frac{200}{30} = \frac{20}{3} \approx 6.67 \text{ seconds} \]

### Final Answer
The time taken for the two trains to cross each other is approximately **6.67 seconds**.

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