A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

We are given:

• Person A walks at 4.5 km/h and is overtaken in 8.4 seconds
• Person B walks at 5.4 km/h and is overtaken in 8.5 seconds
• Both persons walk in the same direction as the train
• Let the speed of the train be x km/h

Step 1: Use the relative speed concept

Train length (L) = Relative speed × Time
For person A:
L = (x - 4.5) × (5 / 18) × 8.4

For person B:
L = (x - 5.4) × (5 / 18) × 8.5

Step 2: Set both expressions equal (since train length is same)

(x - 4.5) × 8.4 = (x - 5.4) × 8.5

Step 3: Solve the equation

8.4x - 37.8 = 8.5x - 45.9
=> 45.9 - 37.8 = 8.5x - 8.4x
=> 8.1 = 0.1x
=> x = 81 km/hr

Final Answer:

The speed of the train is 81 km/hr