Calculating Moving Train Speed

This problem involves calculating the speed of a moving train based on its length, the length of a stationary train it crosses, and the time taken to cross.

Understanding the Concept

When a moving train crosses a stationary object (like a stationary train, platform, or tunnel), the total distance the moving train needs to cover is the sum of its own length and the length of the stationary object.

The formula relating speed, distance, and time is:

$Speed = Distance / Time$

Step-by-Step Solution

1. Identify Given Information:
   • Length of the moving train = 120 m
   • Length of the stationary train = 80 m
   • Time taken to cross = 8 seconds
2. Calculate Total Distance:

   The total distance the moving train covers to completely cross the stationary train is the sum of their lengths.

   $Total Distance = Length of moving train + Length of stationary train$

   $Total Distance = 120 m + 80 m = 200 m$

3. Calculate Speed in meters per second (m/s):

   Using the formula $Speed = Distance / Time$:

   $Speed = 200 m / 8 s$

   $Speed = 25 m/s$

4. Convert Speed to kilometers per hour (km/hr):

   To convert speed from m/s to km/hr, we multiply by the conversion factor $(18/5)$.

   $Speed (km/hr) = Speed (m/s) × (18 / 5)$

   $Speed (km/hr) = 25 × (18 / 5)$

   $Speed (km/hr) = 5 × 18$

   $Speed (km/hr) = 90 km/hr$

Conclusion

Therefore, the speed of the moving train is 90 km/hr.