A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

Given

• Two pedestrians walk in the same direction at 2 km/h and 4 km/h.
• The train completely overtakes them in 9 s and 10 s respectively.

Let the train's speed be v km/h and its length be L metres.

Relative-speed method
When overtaking the 2 km/h walker: L = (v − 2) × (5/18) × 9 = (5/2)(v − 2)When overtaking the 4 km/h walker: L = (v − 4) × (5/18) × 10 = (25/9)(v − 4)Equate: (5/2)(v − 2) = (25/9)(v − 4)⇒ 9(v − 2) = 10(v − 4) ⇒ v = 22 km/hNow L = (5/2)(22 − 2) = 50 m

Final Answer:
The train's length is 50 m.