Find the time taken by a train of length 100 m running at a speed of 72 kmph to cross another train of length 200 m running at a speed of 63 kmph in the same direction

Options

A. 60 s
B. 30 s
C. 120 s
D. 90 s

Answer

To solve the problem of finding the time taken by a train of length 100 m running at a speed of 72 km/h to cross another train of length 200 m running at a speed of 63 km/h in the same direction, we can follow these steps:

### Step 1: Convert the speeds from km/h to m/s
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).

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

- Speed of the second train:
\[ 63 \text{ km/h} = 63 \times \frac{5}{18} = 17.5 \text{ m/s} \]

### Step 2: Calculate the relative speed of the two trains
Since both trains are moving in the same direction, the relative speed is the difference between their speeds.

\[ \text{Relative speed} = \text{Speed of first train} - \text{Speed of second train} = 20 \text{ m/s} - 17.5 \text{ m/s} = 2.5 \text{ m/s} \]

### Step 3: Calculate the total distance to be covered
The total distance to be covered when one train crosses the other is the sum of their lengths.

\[ \text{Total distance} = \text{Length of first train} + \text{Length of second train} = 100 \text{ m} + 200 \text{ m} = 300 \text{ m} \]

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

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we found:

\[ \text{Time} = \frac{300 \text{ m}}{2.5 \text{ m/s}} = 120 \text{ seconds} \]

### Final Answer
The time taken by the first train to cross the second train is **120 seconds**.

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