Train vs Person

Level pending

A train travels at 7 times the speed of a runner. If it takes 8 seconds for the entire train to pass the runner when they are traveling in the same direction, how long will it take for the entire train to pass the runner when they are traveling in opposite directions?


The answer is 6.

Shevy Doc by Shevy Doc , 16, Australia

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1 solution

Pop Wong
Aug 29, 2020

Assumptions:

  • Their speeds are far below than the speed of light
  • They start at head to head position
  • V r V_r be the speed of the runner
  • V t = 7 V r V_t = 7 V_r be the speed of the train
  • L L be the length of the train
  • t t be the time required for the entire train to pass the runner in opposite direction

Traveling in the same direction, the relative speed of the train to the runner = 7 V r − V r = 6 V r = 7V_r - Vr = 6 V_r

Traveling in the opp. direction, the relative speed of the train to the runner = 7 V r + V r = 8 V r = 7V_r + Vr = 8 V_r

\[6 V_r \cdot 8 = L = 8 V_r \cdot t \\

\boxed{t = 6} \]

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