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) using the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]

- For the first train (72 km/h):
\[ \text{Speed}_1 = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

- For the second train (36 km/h):
\[ \text{Speed}_2 = 36 \times \frac{5}{18} = 10 \text{ m/s} \]

### Step 2: Calculate the total distance to be covered
Both trains have a length of 100 meters each. When they cross each other, the total distance that needs to be covered is the sum of their lengths:
\[ \text{Total Distance} = 100 \text{ m} + 100 \text{ m} = 200 \text{ m} \]

### Step 3: Calculate the relative speed
Since the trains are moving towards each other, we can add their speeds to find the relative speed:
\[ \text{Relative Speed} = \text{Speed}_1 + \text{Speed}_2 = 20 \text{ m/s} + 10 \text{ m/s} = 30 \text{ m/s} \]

### Step 4: Calculate the time taken to cross each other
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can substitute the total distance and the relative speed:
\[ \text{Time} = \frac{200 \text{ m}}{30 \text{ m/s}} \approx 6.67 \text{ seconds} \]

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

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