Shortcut Trick
When two trains of equal length cross a pole in t1 and t2 seconds respectively.
Time taken to cross each other in same direction = [2 × t1 × t2] ÷ [t2 − t1]
⇒ Time = [2 × 13 × 26] ÷ [26 − 13]
⇒ Time = [2 × 13 × 26] ÷ 13 = 2 × 26 = 52 seconds.
∴ The correct answer is 52 sec.
Alternate Method
Given:
Length of each train = L (Let LCM of 13 and 26 = 26 units)
Time taken by Train 1 = 13 sec | Time taken by Train 2 = 26 sec
Formula Used:
Speed = Distance ÷ Time | Relative Speed (Same Direction) = S1 − S2
Calculations:
⇒ Let length of each train (L) = 26 m
⇒ Speed of Train 1 (S1) = 26 ÷ 13 = 2 m/s
⇒ Speed of Train 2 (S2) = 26 ÷ 26 = 1 m/s
⇒ Relative Speed = S1 − S2 = 2 − 1 = 1 m/s
⇒ Total distance to cross each other = L + L = 26 + 26 = 52 m
⇒ Time taken = Total Distance ÷ Relative Speed = 52 ÷ 1 = 52 seconds
∴ The correct answer is 52 sec.
Additional Information
Relative Speed in Opposite Direction
When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S1 + S2).
Crossing a Stationary Object
To cross a pole or a person, a train must cover a distance equal to its own length (L). To cross a platform of length P, it must cover (L + P).
Unit Conversion
To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.