Multiple choice

A $100\ m$ long train at $15 m/s$ overtakes a man running on the platform in the same direction in $10\ s$. How long the train will take top cross the man if he was running in the opposite direaction?

  1. $7\ s$
  2. $5\ s$
  3. $3\ s$
  4. $1\ s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When the man runs in the same direction, the relative speed is 100/10 = 10 m/s, so his speed is 15 - 10 = 5 m/s. Running in the opposite direction gives a relative speed of 15 + 5 = 20 m/s, so the crossing time is 100/20 = 5 seconds.

AI explanation

When the train overtakes the man running in the same direction, the relative speed is the length of the train divided by the time taken, yielding 100 m divided by 10 s = 10 m/s. Since the actual speed of the train is 15 m/s, the speed of the man is 15 m/s minus 10 m/s, which equals 5 m/s. If the man runs in the opposite direction, their relative speed becomes the sum of their speeds, giving 15 m/s + 5 m/s = 20 m/s. The time taken to cross the man is the length of the train divided by this new relative speed, resulting in 100 m divided by 20 m/s, which is 5 s.

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