Question
Download Solution PDFA 250 m long train overtakes a man moving at a speed of 7 km/h (in same direction) in 36 seconds. How much time (in seconds) will it take this train to completely cross another 415 m long train, moving in the opposite direction at a speed of 82 km/h?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A 250 m long train overtakes a man moving at a speed of 7 km/h (in same direction) in 36 seconds.
Another 415 m long train is moving in the opposite direction at a speed of 82 km/h.
Formula used:
Relative Speed (same direction) = Speed of Train - Speed of Man
Speed = Distance / Time
Relative Speed (opposite direction) = Speed of Train + Speed of Another Train
Time to cross = Total Distance / Relative Speed
Calculation:
First, find the speed of the train:
Let the speed of the train be x km/h.
Relative Speed (same direction) = x - 7 km/h.
Distance = 250 m = 0.25 km.
Time = 36 seconds = 36/3600 hours = 0.01 hours.
Speed = Distance / Time
⇒ x - 7 = 0.25 / 0.01
⇒ x - 7 = 25
⇒ x = 32 km/h
Next, find the time to cross the other train:
Relative Speed (opposite direction) = 32 + 82 = 114 km/h.
Total Distance = 250 m + 415 m = 665 m = 0.665 km.
Time to cross = Total Distance / Relative Speed
⇒ Time = 0.665 / 114
⇒ Time = 0.00583 hours
⇒ Time = 0.00583 × 3600 seconds
⇒ Time ≈ 21 seconds
∴ The correct answer is option (4).
Last updated on Jun 2, 2025
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