Two trains 319 m and 377 m long are running in same direction with the speeds…

Concept: Two bodies moving along parallel paths in the SAME direction close or open the gap between them only at the difference of their speeds, so the relative speed is (faster speed − slower speed). Two trains are completely clear of each other when the relative displacement between them equals the SUM of their two lengths, because the rear of the overtaking train must travel past the front of the other train.

Applying this to the given data:

1. Relative speed (same direction) = 37 m/s − 25 m/s = 12 m/s.

2. Distance to be covered relative to each other = sum of the lengths = 319 m + 377 m = 696 m.

3. Time to be clear = relative distance ÷ relative speed = 696 m ÷ 12 m/s = 58 seconds.

Cross-check by absolute distances: in 58 s the faster train travels 37 × 58 = 2146 m and the slower train travels 25 × 58 = 1450 m. The faster train therefore gains 2146 − 1450 = 696 m on the slower one, exactly the combined length of the two trains, so 58 seconds is confirmed.

Contrast: had the two trains been running in OPPOSITE directions, the gap would close at 37 + 25 = 62 m/s and the same 696 m would be cleared in 696 ÷ 62 ≈ 11.2 s. The lengths are unchanged; only the direction of travel changes the rate at which the relative distance is covered.