This is a relative speed problem involving train lengths, and the trick is figuring out exactly what distance the faster train needs to cover relative to the slower one.
Step 1: Understand what "overtake" means here.
The problem says: from the moment the front of the faster train reaches the back of the slower train, to the moment the last carriage of the faster train clears the front of the slower one. That means the faster train needs to travel the entire length of the slower train PLUS its own entire length, relative to the slower train.
Step 2: Calculate the total relative distance.
Total distance = length of slower train + length of faster train = 160 + 240 = 400 meters.
Step 3: Calculate relative speed.
Since both trains move in the same direction:
Relative speed = 72 - 48 = 24 km/h.
Convert to m/s: 24 × 1000/3600 = 20/3 m/s ≈ 6.67 m/s.
Step 4: Calculate time.
Time = Distance ÷ Speed = 400 ÷ (20/3) = 400 × 3/20 = 60 seconds.
Answer: B (60 seconds)
Common trap: The biggest mistake is only adding one train's length instead of both. Students think "the faster train just needs to pass the slower one," so they use only 160 meters (the slower train's length). But re-read the problem: it asks until the LAST carriage of the faster train clears the FRONT of the slower one — so the faster train's full 240 meters also need to clear.
Takeaway: On train-passing problems, always sketch a quick diagram and ask: what is the starting position and ending position of the reference point? The total relative distance is always the sum of both objects' lengths when one fully passes the other.