A 275 m long train overtakes a man moving at a speed of 6 km/h (in same direction) in 45 seconds. How much time (in seconds) will it take this train to completely cross another 280 m long train, moving in the opposite direction at a speed of 26 km/h?

Given:

A 275 m long train overtakes a man moving at a speed of 6 km/h (in the same direction) in 45 seconds.

Another train length = 280 m, moving in the opposite direction at a speed of 26 km/h.

Formula used:

Relative speed (same direction) = Speed of train - Speed of man

Relative speed (opposite direction) = Speed of train + Speed of other train

Distance = Speed × Time

Calculation:

Speed of man = 6 km/h = 6 × (5/18) m/s = 5/3 m/s

Relative speed (same direction) = Speed of train - Speed of man

⇒ (Speed of train - 5/3) m/s = Distance / Time

⇒ (Speed of train - 5/3) = 275 / 45

⇒ Speed of train = (275 / 45) + 5/3

⇒ Speed of train = 350 / 45 m/s = 7.78 m/s

Relative speed (opposite direction) = Speed of train + Speed of other train

Speed of other train = 26 km/h = 26 × (5/18) m/s = 7.22 m/s

⇒ Relative speed = 7.78 + 7.22 = 15 m/s

Combined length of both trains = 275 m + 280 m = 555 m

Time = Distance / Speed

⇒ Time = 555 / 15 = 37 seconds

∴ The correct answer is option (2).