A train traveling at 136 km/h completely crosses another train having half its length and traveling in the opposite direction at 44 km/h in 6 s. If it also passes a railway platform in 45 s, then ¹ find the length of the platform. (In m)

Given:

Speed of Train 1 = 136 km/h

Speed of Train 2 = 44 km/h

Time taken to cross Train 2 = 6 s

Time taken to cross the platform = 45 s

Length of Train 1 = L₁

Length of Train 2 = L₂ = L₁/2

Find the length of the platform.

Formula Used:

Relative Speed (in m/s) = (Speed of Train 1 + Speed of Train 2) × (5/18)

Distance = Speed × Time

Calculation:

Relative Speed of trains = (136 + 44) × (5/18)

⇒ Relative Speed = 180 × (5/18)

⇒ Relative Speed = 50 m/s

Distance covered to cross Train 2 = Relative Speed × Time

⇒ L₁ + L₂ = 50 × 6

⇒ L₁ + L₁/2 = 300

⇒ (3L₁/2) = 300

⇒ L₁ = (300 × 2)/3

⇒ L₁ = 200 m

Speed of Train 1 (in m/s) = 136 × (5/18)

⇒ Speed = 37.78 m/s

Distance covered to cross the platform = Speed × Time

⇒ L₁ + Platform Length = 37.78 × 45

⇒ 200 + Platform Length = 1700

⇒ Platform Length = 1700 - 200

⇒ Platform Length = 1500 m

The length of the platform is 1500 m.