What was the speed of the train?

Determining Train Speed: A Three-Variable Formula

Calculating a train's speed involves understanding the relationship between its length, the platform it passes, and the time it takes to traverse the platform's length. This relationship can be expressed using a simple formula:

Speed = Train Length / (Platform Length / Time)

Components of the Formula:

• Train Length: The length of the train in meters, feet, or other units of distance.

• Platform Length: The length of the platform in the same units as the train length.

• Time: The time it takes for the entire train to pass the platform in seconds, minutes, or other units of time.

Derivation of the Formula:

As the train moves, the distance it covers is equal to its own length plus the length of the platform. This distance is equal to the speed of the train multiplied by the time taken to cover it. Thus, we can derive the formula:

Distance = Train Length + Platform Length
Distance = Speed × Time
Speed = (Train Length + Platform Length) / Time
Speed = Train Length / (Platform Length / Time)

Example:

Suppose a train with a length of 200 meters passes a platform with a length of 100 meters in 30 seconds. To calculate its speed:

• Train Length = 200 meters
• Platform Length = 100 meters
• Time = 30 seconds

Using the formula:

Speed = Train Length / (Platform Length / Time)
Speed = 200 meters / (100 meters / 30 seconds)
Speed = 200 meters / 3.33 meters per second
Speed = 60 meters per second

Therefore, the train's speed is 60 meters per second.

Note:

It's important to ensure that the units used for train length, platform length, and time are consistent. For example, if the train length is given in feet and the platform length is given in meters, the platform length should be converted to feet before performing the calculation.