The speed of a train $T$ is $100$ km per hour and the speed of a person $P$ is $4$ km per hour. $T$ crosses $P$ in $15$ seconds, if $P$ travels along the direction of motion of $T$. If $P$ travels along the opposite direction of $T$, then in how much time does $T$ cross $P$, in seconds, approximately?
Detailed Explanation:
Same-direction crossing: Relative speed = 100 - 4 = 96 km/h = 80/3 m/s. Train length L = (80/3) × 15 = 400 m.
Opposite-direction crossing: Relative speed = 100 + 4 = 104 km/h = 260/9 m/s. Time = 400 ÷ (260/9) = 3600/260 ≈ 13.846 seconds.
Therefore, the train crosses in approximately 13.85 seconds, making Option 3 the correct answer.
Question 1 of 5 Time, Speed & Distance
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