A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

Step 1: Understand the given data

• Time taken to pass a telegraph post = 8 seconds
• Time taken to pass a bridge = 20 seconds
• Length of the bridge = 264 meters

Step 2: Let the length of the train be L meters

• When the train passes the telegraph post, it covers its own length in 8 seconds
• So, L = Speed × 8 → Speed = L / 8

Step 3: When it passes the bridge

• Total distance covered = Length of train + Length of bridge = L + 264
• Time taken = 20 seconds
• So, (L + 264) = Speed × 20 = (L / 8) × 20

Step 4: Solve the equation

L + 264 = (L / 8) × 20
L + 264 = (20L) / 8
L + 264 = (5L) / 2

Multiply both sides by 2:
2L + 528 = 5L
528 = 5L - 2L
528 = 3L
L = 176 meters

Step 5: Find the speed of the train

Speed = L / 8 = 176 / 8 = 22 m/s
Convert to km/hr: 22 × 18 / 5 = 79.2 km/hr

Answer: The speed of the train is 79.2 km/hr

This is a classic speed–distance–time problem where the trick is to understand that when a train crosses a point (like a pole), it covers its own length, and when it crosses a bridge, it covers its own length plus the bridge length. Problems like this test your algebraic setup and unit conversion skills.