A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

Given

• Time to pass a pole (i.e., a point) = 15 s
• Time to pass a 100 m platform = 25 s
• Let train length = L meters and speed = v m/s

Key Relations

Passing a pole ⇒ Distance = L = v × 15 … (1) Passing a platform ⇒ Distance = L + 100 = v × 25 … (2)

Step 1: Eliminate v to find speed
(2) − (1): (L + 100) − L = v×25 − v×15 100 = 10v ⇒ v = 10 m/s

Step 2: Find train length
From (1): L = v × 15 = 10 × 15 = 150 m

Final Answer
The length of the train is 150 m.