Multiple choice

A train $75$ m long overtook a person who was walking at the rate of $6$ km/hr and passes him in $\displaystyle 7\frac{1}{2}$ seconds. Subsequently it overtook a second person and passed him in $\displaystyle 6\frac{3}{4}$ seconds. At what rate was the second person travelling?

  1. $4$ km/hr
  2. $1$ km/hr
  3. $2$ km/hr
  4. $5$ km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train speed v, person speed u. Relative speed = 75 / (15/2) = 10 m/s = 36 km/hr. v - 6 = 36, so v = 42 km/hr. Second person time = 27/4 seconds. Relative speed = 75 / (27/4) = 300/27 = 100/9 m/s = (100/9) * 3.6 = 40 km/hr. v - u2 = 40. 42 - u2 = 40, so u2 = 2 km/hr.

AI explanation

Convert the overtaking time of the first person to 7.5 seconds, and use the relative speed formula to find the train's speed. The relative speed to the first person is 75 meters divided by 7.5 seconds, giving 10 m/s, which equals 36 km/hr; adding the person's walking speed of 6 km/hr gives a train speed of 42 km/hr. For the second person, the relative speed is 75 divided by 6.75 seconds, which is 100/9 m/s, or 40 km/hr. Subtracting this relative speed from the train's total speed gives 42 minus 40, resulting in a second person's speed of 2 km/hr.

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