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?

Given Data

• Two walkers at 4.5 km/hr and 5.4 km/hr (same direction as the train)
• Train overtakes them in 8.4 s and 8.5 s respectively
• Required: speed of the train

Step 1: Set up equationsLet train speed = v km/hr and train length = L m.L = 8.4 × (v − 4.5) × (5/18)L = 8.5 × (v − 5.4) × (5/18)

Step 2: Eliminate L and solve for v8.4(v − 4.5) = 8.5(v − 5.4)8.4v − 37.8 = 8.5v − 45.90.1v = 8.1 ⇒ v = 81 km/hr

Checks & Common Pitfalls

• Same direction with pedestrians uses the difference of speeds.
• Keep seconds and km/hr consistent by using the 5/18 factor.

Final AnswerThe speed of the train is 81 km/hr.