https://file.aiquickdraw.com/mathbot/file/1732621625959v69r3ut8.jpg

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.

A train passes through a station at a speed of 108 km/h. The length of the station is 120 m. The train takes 7 seconds to completely pass through the station. Work out the length of the train.

Solve the problem of finding the length of a train passing through a 120-meter-long station at 108 km/h in 7 seconds. Includes step-by-step calculations using the distance formula and unit conversions. Suitable for Grade 8-10 students.

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