Two trains, each 120 m long, moving in opposite directions, cross each other…
2023
Two trains, each 120 m long, moving in opposite directions, cross each other in 12 seconds. If one train moves twice as fast as the other, then the speed (in km/hr) of the faster train is:
- A.
24
- B.
60
- C.
48
- D.
36
Show answer & explanation
Correct answer: C
Concept:
When two bodies move in opposite directions, their relative speed equals the sum of their individual speeds. When two trains cross each other completely, the total distance covered equals the sum of their lengths, and time taken = total distance / relative speed.
Application:
Let the speed of the slower train be x m/s, so the faster train's speed is 2x m/s, since it moves twice as fast.
Since the trains move in opposite directions, their relative speed = x + 2x = 3x m/s.
The total distance to be covered while crossing = sum of both train lengths = 120 m + 120 m = 240 m.
Using time = distance / speed: 12 = 240 / 3x, so 3x = 240 / 12 = 20 m/s.
Solving, x = 20/3 m/s, so the faster train's speed = 2x = 40/3 m/s.
Converting to km/hr: 40/3 m/s x 18/5 = 720/15 = 48 km/hr.
Cross-check:
At a combined rate of 20 m/s (found above), the two trains together cover 20 x 12 = 240 m in 12 seconds -- exactly the combined length of both trains (120 m + 120 m), confirming the value found.
