Two trains, A and B, are moving in the same direction on parallel tracks. The…
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Two trains, A and B, are moving in the same direction on parallel tracks. The speed of train A is 160 kmph, and the speed of train B is 70 kmph. The length of train B is 72 meters. Train A completely overtakes train B in 5 seconds. Find the length of train A.
- A.
53 m
- B.
50 m
- C.
48 m
- D.
85 m
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Correct answer: A
Key steps:
Find the relative speed of the two trains: 160 km/h − 70 km/h = 90 km/h.
Convert the relative speed to metres per second: multiply by 5/18. So 90 × 5/18 = 25 m/s.
Distance covered relative to the other train in 5 s = speed × time = 25 × 5 = 125 m.
This distance equals the sum of the lengths of the two trains. So length of train A = 125 m − length of train B (72 m) = 53 m.
Answer: Length of train A = 53 m
Shortcut: (Relative speed in m/s) × Time = Sum of lengths, so subtract the known length of the slower train to get the required length.