Shortcut Trick
Relative Speed in opposite direction = S1 + S2 = 70 + 38 = 108 km/hr.
Convert Speed to m/s: 108 × (5/18) = 30 m/s.
Total Distance to cover = Sum of lengths = 380 + 160 = 540 m.
Time = Distance ÷ Relative Speed = 540 ÷ 30 = 18 sec.
∴ The correct answer is 18 sec.
Alternate Method
Given:
Length of Train 1 (L1) = 380 m
Length of Train 2 (L2) = 160 m
Speed of Train 1 (S1) = 70 km/hr
Speed of Train 2 (S2) = 38 km/hr
Formula Used:
Time = (L1 + L2) ÷ (Relative Speed)
Relative Speed (Opposite Direction) = S1 + S2
Calculations:
⇒ Total distance to be covered = 380 + 160 = 540 m
⇒ Relative speed = 70 + 38 = 108 km/hr
⇒ Converting speed into m/s = 108 × (5/18) m/s
⇒ Relative speed = 6 × 5 = 30 m/s
⇒ Time taken = 540 ÷ 30
⇒ Time taken = 18 seconds
∴ The correct answer is 18 sec.
Additional Information
Relative Speed Concept
When two objects move in opposite directions, their relative speed is the sum of their individual speeds (u + v). When they move in the same direction, it is the difference (u − v).
Unit Conversion
To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.
Crossing Distance
When a train crosses another train or a bridge, the total distance is the sum of their lengths. When it crosses a pole or a person, the distance is simply the length of the train itself.