To solve the problem, we can use the relationship:

Distance = Speed × Time

Step 1: Convert speed to meters per second

The train's speed is given as 108 km/h. Converting it to meters per second:

$1 \, \text{km/h} = \frac{1000}{3600} \, \text{m/s} = \frac{5}{18} \, \text{m/s}$

So:

$108 \, \text{km/h} = 108 \times \frac{5}{18} \, \text{m/s} = 30 \, \text{m/s}$

Step 2: Total distance covered

The train completely passes the station in 7 seconds. During this time, it covers a distance equal to the length of the train plus the length of the station. Using the formula:

$\text{Total distance} = \text{Speed} \times \text{Time}$

$\text{Total distance} = 30 \, \text{m/s} \times 7 \, \text{s} = 210 \, \text{m}$

Step 3: Calculate the length of the train

The total distance is the sum of the length of the train and the length of the station:

$\text{Length of train} + \text{Length of station} = 210 \, \text{m}$

The station length is given as 120 m, so:

$\text{Length of train} = 210 \, \text{m} - 120 \, \text{m} = 90 \, \text{m}$

Final Answer:

The length of the train is 90 meters.

Would you like further clarifications or explanations? Here are five questions to expand your understanding:

1. How is the conversion from km/h to m/s derived?
2. Why is it necessary to add the station length to the train length in the distance calculation?
3. What would change if the train's speed were different?
4. Can this approach be applied to scenarios with curved tracks or varying speeds?
5. How does understanding this type of problem help in real-world applications like traffic flow analysis?

Tip: Always ensure consistent units (e.g., meters and seconds) when solving speed, time, and distance problems.