Question
Download Solution PDFA train takes 11 seconds and 10 seconds to cross 2 men who are walking in the same direction of the train at the speed of 6 km/hr and 5 km/hr respectively. Find the speed of the train.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Time taken to cross the first man = 11 seconds
Time taken to cross the second man = 10 seconds
Speed of the first man = 6 km/hr
Speed of the second man = 5 km/hr
Formula used:
Speed of the train relative to a man = (Speed of train - Speed of man)
Distance covered by the train = Speed of the train × Time
Calculation:
Let the speed of the train be x km/hr.
Relative Speed of Train and First Man:
Relative speed = (x - 6) km/hr = (x - 6) × 5/18 m/s
Distance covered in crossing = (x - 6) × 5/18 × 11 meters
Relative Speed of Train and Second Man:
Relative speed = (x - 5) km/hr = (x - 5) × 5/18 m/s
Distance covered in crossing = (x - 5) × 5/18 × 10 meters
Since the distance covered by the train in both cases is the same:
(x - 6) × 11 = (x - 5) × 10
Simplifying the equation:
11x - 66 = 10x - 50
11x - 10x = 66 - 50
x = 16 km/hr
∴ The speed of the train is 16 km/hr.
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