A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

Step 1: Understand the problem

• The train passes a pole in 15 seconds.
• The train passes a platform of 100 meters in 25 seconds.
• We need to find the length of the train.

Step 2: Find the speed of the train

• When a train passes a pole, it covers a distance equal to its own length.
• Let the length of the train be L meters.
• Speed of the train = L / 15 (in m/s)

Step 3: Use platform data to form an equation

• When the train passes a platform, it covers (Length of train + Length of platform).
• Time taken = 25 seconds
• Total distance = L + 100
• Speed = (L + 100) / 25

Step 4: Equating both expressions for speed

L / 15 = (L + 100) / 25

Cross-multiply:
25L = 15(L + 100)
25L = 15L + 1500
25L - 15L = 1500
10L = 1500
L = 150

Answer: The length of the train is 150 meters.

This problem highlights how to apply the distance = speed × time formula in scenarios where a moving object (train) crosses a stationary object (pole or platform). The key is to set up the equations correctly and solve for the unknown.