How many seconds will a 500 meter long train moving with a speed of 63 km/hr,…

2023

How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?

  1. A.

    42

  2. B.

    50

  3. C.

    30

  4. D.

    28

Attempted by 1 students.

Show answer & explanation

Correct answer: C

Step-by-Step Solution

To find the time taken for the train to cross the man, we need to determine their relative speed and convert it into compatible units.

  1. Calculate Relative Speed:

    • Since the man and the train are moving in the same direction, the relative speed is the difference between their speeds.

    • Relative Speed = Speed of Train - Speed of Man

    • Relative Speed = 63 km/hr - 3 km/hr = 60 km/hr.

  2. Convert Speed to Meters per Second (m/s):

    • To convert km/hr to m/s, multiply by 5/18.

    • Relative Speed = 60 * (5/18) m/s

    • Relative Speed = 300 / 18 m/s = 50/3 m/s.

  3. Calculate Time Taken:

    • The distance to be covered to "cross" the man is equal to the length of the train (500 meters).

    • Time = Distance / Relative Speed

    • Time = 500 / (50/3)

    • Time = 500 * (3/50) = 10 * 3 = 30 seconds.

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