A train overtakes two people walking along the track in the same direction at 4.5 km/h and 5.4 km/h, respectively. It takes 8.4 s to overtake the first and 8.5 s to overtake the second. Assuming uniform speed and length for the train, find the train’s speed (km/h).

Introduction / Context:
In same-direction overtaking, relative speed equals (train speed − walker speed). The time to overtake equals train length divided by relative speed. Equal train length in both cases lets us equate two expressions and solve for the train’s speed.

Given Data / Assumptions:

• Walker speeds: 4.5 km/h and 5.4 km/h.
• Overtaking times: 8.4 s and 8.5 s.
• Train length = constant; uniform speed.

Concept / Approach:
Let train speed be V (km/h) and length be L (m). Convert to m/s when multiplying by seconds. For same direction,L = (V − 4.5) * 5/18 * 8.4 = (V − 5.4) * 5/18 * 8.5.Cancel 5/18 and solve for V.

Step-by-Step Solution:

Verification / Alternative check:
Compute implied length: L = (81 − 4.5) * 5/18 * 8.4 ≈ 178.5 m. Using the other case with 8.5 s gives the same L, confirming consistency.

Why Other Options Are Wrong:
66, 72, 78, 60 km/h fail the equality of lengths or produce inconsistent train lengths across the two overtakings.

Common Pitfalls:
Adding speeds (opposite direction rule) or leaving speeds in km/h when multiplying by seconds (unit mismatch).

Final Answer:
81 km/h