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

To solve the problem, let's break it down step by step:

### Given Data:
- Speed of the train = 108 km/h
- Length of the station = 120 meters
- Time to completely pass the station = 7 seconds

### Step 1: Convert the speed of the train to meters per second (m/s).
Since the time is given in seconds and the length in meters, we need to work in meters per second (m/s).

\[
\text{Speed} = 108 \, \text{km/h} = \frac{108 \times 1000}{3600} \, \text{m/s} = 30 \, \text{m/s}
\]

### Step 2: Use the formula for distance.
The total distance covered by the train while passing the station consists of the length of the train plus the length of the station. We can calculate this total distance using the speed of the train and the time taken to pass:

\[
\text{Distance covered in 7 seconds} = \text{Speed} \times \text{Time}
\]

\[
\text{Distance} = 30 \, \text{m/s} \times 7 \, \text{seconds} = 210 \, \text{meters}
\]

### Step 3: Calculate the length of the train.
The total distance covered is the length of the train plus the length of the station, which means:

\[
\text{Total distance} = \text{Length of the train} + \text{Length of the station}
\]

\[
210 = \text{Length of the train} + 120
\]

\[
\text{Length of the train} = 210 - 120 = 90 \, \text{meters}
\]

### Conclusion:
The length of the train is **90 meters**.

Would you like more details or have any other questions?

Here are some related questions to explore:
1. What would the time taken be if the train length were 100 meters instead?
2. If the speed of the train were reduced to 54 km/h, how long would it take to pass the same station?
3. What is the relation between speed, time, and distance in such problems?
4. How would the time change if the station were 50% longer?
5. Can this problem be solved using relative motion concepts?

**Tip:** Always ensure units are consistent (e.g., converting km/h to m/s) when working with speed, distance, and time.

Learn how to calculate the length of a train that passes through a station at 108 km/h, with a station length of 120m, taking 7 seconds to pass. This detailed solution uses key concepts of speed, time, and distance, and is ideal for students in Grades 6-8.

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