A man sees a train passing over a bridge 1 km long. The length of the train is half that of the
bridge. If the train clears the bridge in 2 minutes, the speed of the train is

The problem involves determining the speed of a train that crosses a bridge.

### Step-by-step solution:

1. **Length of the bridge** = 1 km (or 1000 meters).
2. **Length of the train** = half the length of the bridge, which means:
   \[
   \text{Length of the train} = \frac{1}{2} \times 1000 = 500 \, \text{meters}
   \]
3. **Total distance covered by the train** = length of the train + length of the bridge. To completely cross the bridge, the train must travel a distance equal to the sum of its length and the bridge's length:
   \[
   \text{Total distance} = 1000 \, \text{meters} + 500 \, \text{meters} = 1500 \, \text{meters}
   \]
4. **Time taken** = 2 minutes = \(2 \times 60 = 120 \, \text{seconds}\)
   
5. Now, we can use the formula for speed:
   \[
   \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{1500 \, \text{meters}}{120 \, \text{seconds}} = 12.5 \, \text{m/s}
   \]

6. Finally, convert the speed from meters per second to kilometers per hour:
   \[
   \text{Speed in km/h} = 12.5 \times \frac{3600}{1000} = 45 \, \text{km/h}
   \]

### Conclusion:
The speed of the train is **45 km/h**.

Would you like more details or have any questions about this?

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Here are 5 related questions for further exploration:
1. What would be the train's speed if it cleared the bridge in 3 minutes instead of 2?
2. How would the speed change if the bridge length was doubled but the train's length stayed the same?
3. If the train's speed were doubled, how much time would it take to clear the same bridge?
4. How does the train's length impact the total time taken to clear the bridge?
5. How would you calculate the speed if the time taken was given in fractions of a minute?

**Tip**: When converting between units, always ensure you're using consistent units throughout the calculation (e.g., meters and seconds or kilometers and hours).

A man sees a train passing over a bridge 1 km long. The length of the train is half that of the bridge. If the train clears the bridge in 2 minutes, the speed of the train is

Determine the speed of a train that crosses a 1 km bridge in 2 minutes. This problem uses kinematic concepts of speed, distance, and time and includes step-by-step calculations, including unit conversion. Ideal for Grades 6-8.

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