Shortcut Trick
Relative Speed in same direction = 40 − 30 = 10 km/h.
Total Distance to cover = Sum of train lengths = 250 + 400 = 650 m.
Convert speed to m/s: 10 × (5/18) = 25/9 m/s.
Time in seconds = Distance ÷ Speed = 650 ÷ (25/9) = 234 s.
Time in minutes = 234 ÷ 60 = 3.9 min.
∴ The correct answer is 3.9 min.
Alternate Method
Given:
Length of first train (L1) = 250 m, Speed (S1) = 40 km/h
Length of second train (L2) = 400 m, Speed (S2) = 30 km/h
Formula Used:
Time = (L1 + L2) ÷ (S1 − S2) [When moving in the same direction]
Calculations:
⇒ Total distance = 250 + 400 = 650 m
⇒ Relative speed = (40 − 30) × (5/18) m/s
⇒ Relative speed = 10 × (5/18) = 25/9 m/s
⇒ Time taken = 650 ÷ (25/9) seconds
⇒ Time taken = (650 × 9) ÷ 25 = 26 × 9 = 234 seconds
⇒ Converting seconds to minutes: 234 ÷ 60
⇒ Time taken = 3.9 min
∴ The correct answer is 3.9 min.
Additional Information
Relative Speed Rules
When two objects move in the same direction, relative speed = S1 − S2. When they move in opposite directions, relative speed = S1 + S2.
Unit Conversion
To convert speed from km/h to m/s, multiply by 5/18. To convert from m/s to km/h, multiply by 18/5.
Total Distance for Trains
While crossing each other, the total distance is always the sum of the lengths of both trains, regardless of the direction of motion.