Question
Download Solution PDFThe length of a train is 150 metres. In 3 seconds, it passes a man travelling at 2 km/h in the same direction as the train. Determine the train's speed.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFData:
Length of the train (L) = 150 meters
Time taken to pass the man (t) = 3 seconds
Speed of the man (Sm) = 2 km/h = 0.56 m/s
Concept:
Relative speed is same direction = Speed of a train - Speed of a Man.
Speed = Distance/Time,
Solution:
Assume the speed of the train to be x km/h.
When travelling in the same direction, the relative speed is (x - 2) km/h.
Convert this relative speed from km/h to m/s.
⇒ Relative speed = (x - 2) × (5/18) m/s
We know the train covers 150 m distance in 3 sec.
According to the formula, Speed = Distance/Time,
the relative speed = 150/3 = 50 m/s
Now, equate the two expressions for relative speed:
⇒ (x - 2) × (5/18) = 50
Solving this equation for x:
⇒ x - 2 = 50 × (18/5)
⇒ x - 2 = 180
⇒ x = 180 + 2 = 182
Therefore, the speed of the train is 182 km/h.
Last updated on Jun 12, 2025
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