Shortcut Trick
Total distance to cross = 370 + 330 = 700 m
Relative speed (same direction) = 150 − 90 = 60 km/h
Speed in m/min = (60 × 1000) ÷ 60 = 1000 m/min
Time taken = Distance ÷ Speed = 700 ÷ 1000 = 0.7 minutes
∴ The correct answer is 0.7 minutes.
Alternate Method
Given:
Length of slower train (L1) = 370 m
Length of faster train (L2) = 330 m
Speed of slower train (S1) = 90 km/h
Speed of faster train (S2) = 150 km/h
370 m
90 km/h →
330 m
150 km/h →
Total Distance = 700 m
Formula Used:
Time = Total Distance ÷ Relative Speed
Relative Speed (same direction) = S2 − S1
Speed in m/s = Speed in km/h × (5 ÷ 18)
Calculations:
⇒ Total Distance = 370 + 330 = 700 m
⇒ Relative Speed = 150 − 90 = 60 km/h
⇒ Relative Speed in m/s = 60 × (5 ÷ 18) = 50 ÷ 3 m/s
⇒ Time taken in seconds = 700 ÷ (50 ÷ 3)
⇒ Time taken = (700 × 3) ÷ 50 = 42 seconds
⇒ Convert seconds to minutes = 42 ÷ 60
⇒ Time taken = 0.7 minutes
∴ The correct answer is 0.7 minutes.
Additional Information
Relative Speed in Same Direction
When two objects move in the same direction, their relative speed is the difference between their individual speeds: Srelative = |S1 − S2|.
Relative Speed in Opposite Direction
When two objects move in opposite directions, their relative speed is the sum of their individual speeds: Srelative = S1 + S2.
Crossing Objects with Length
When a train crosses another train, a platform, or a bridge, the total distance covered is equal to the sum of the lengths of the train and the object.
Unit Conversion
To convert speed from km/h to m/s, multiply by (5 ÷ 18). To convert speed from m/s to km/h, multiply by (18 ÷ 5).