Two trains 200 meters and 240 meters long are running in the same direction…
2022
Two trains 200 meters and 240 meters long are running in the same direction with speeds of 82 km/hr and 64 km/hr, respectively. In how much time will the first train cross the second?
- A.
88 sec
- B.
44 sec
- C.
64 sec
- D.
84 sec
Attempted by 1 students.
Show answer & explanation
Correct answer: A
When two bodies move in the same direction, the relative speed between them is the difference of their individual speeds, since the faster one is only gaining on the slower one at that reduced rate. To completely cross each other, the faster body must cover a distance equal to the sum of both lengths, measured at this relative speed. A speed in km/hr converts to m/s by multiplying by 5/18.
The trains travel in the same direction, so the relative speed is the difference of their speeds: 82 km/hr minus 64 km/hr = 18 km/hr.
Convert this relative speed to m/s: 18 multiplied by 5/18 = 5 m/s.
To completely cross, the first train must cover a distance equal to the sum of both lengths: 200 m + 240 m = 440 m.
Time taken = distance divided by relative speed = 440 m divided by 5 m/s = 88 seconds.
Cross-check: converting each speed to m/s first gives 82 x 5/18 which is approximately 22.78 m/s and 64 x 5/18 which is approximately 17.78 m/s; their difference is again 5 m/s exactly, confirming the time is 440 divided by 5 = 88 seconds.