Train Crossing Platform Calculation

To solve problems involving a train crossing a platform, the total distance the train must cover includes both its own length and the length of the platform.

Determine Total Distance

First, calculate the total distance the train needs to travel to completely cross the platform.

Train Length = 450 m

Platform Length = 150 m

Total Distance = Train Length + Platform Length

Total Distance = 450 m + 150 m = 600 m

Convert Train Speed

The train's speed is given in kilometers per hour (km/h), but the distances are in meters (m). Convert the speed to meters per second (m/s) for consistency.

Speed = 80 km/h

To convert km/h to m/s, multiply by \frac{5}{18}.

Speed = 80 $\times$ \frac{5}{18} = \frac{400}{18} = \frac{200}{9} m/s

Calculate Time Taken

Now, use the formula Time = Distance / Speed to find the time taken.

Time = \frac{\text{Total Distance}}{\text{Speed}}

Time = \frac{600 \text{ m}}{\frac{200}{9} \text{ m/s}}

Time = 600 $\times$ \frac{9}{200}

Time = 3 $\times$ 9 = 27 s

Therefore, the time taken by the train to cross the platform is 27 seconds.