Two trains are running at 40 km/hr and 20 km/hr respectively in the same…
2023
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. The fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
- A.
25.57 m
- B.
27.77 m
- C.
34.67 m
- D.
39.99 m
Show answer & explanation
Correct answer: B
Concept: When two bodies move in the same direction, the speed at which the faster one gains on / crosses the slower one is the difference of their individual speeds -- this is called the relative speed. To completely cross a person sitting inside the slower train, the faster train must cover a distance equal to its own length, and it does so at this relative speed.
Application:
Fast train speed = 40 km/hr, slow train speed = 20 km/hr; both move in the same direction, and the fast train takes 5 seconds to completely cross the man sitting in the slow train.
Since both trains move in the same direction, relative speed = 40 minus 20 = 20 km/hr.
Convert the relative speed to metres per second: 20 times 5/18 = 100/18 m/s.
Length of the fast train = relative speed times time = (100/18) times 5 = 500/18, which is approximately 27.77 m.
Cross-check: Dividing the obtained length by the relative speed should return the given time: 27.77 divided by (100/18) is approximately 5 seconds, which matches the time stated in the question -- confirming the length is correct.