Quick Review: Races and Games

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Basic Terms
  • Races: A race is a contest of speed in running, riding, driving, sailing, etc for a particular distance.
  • Race Course: The ground or path in which race is conducted is known as a race course.
  • Starting Point: The beginning point of the race is known as starting point.
  • Winning Point: The point where the race is finished is known as winning point.
  • Winner: The contestant who reaches the end point of the race (or finishes the race before all other contestants) is known as the winner.
  • Dead Heat Race: When all the contestants finish the race altogether (i.e. at the same time), then that race is known as dead heat race.
  • Start: Suppose P and Q are two contestants in a race. If before the start of the race, P is at the starting point and Q is ahead of P by 15 meters. Then, we can say that "P gives Q a start of 15 meters".
  • So, to cover a race of 100 meters, P will have to cover 100 meters while Q will have to cover (100-15) = 85 meters.
  • In a 100 meters race, 'P can give Q 12 m' or ‘P beats Q by 12 m' means that while P runs 100 m, Q runs (100-12) = 88 m.
  • Games: 'A game of 100' means that ‘the contestant who comes first in scoring 100 points is the winner’.
  • If P scores 100 points while Q scores only 88 points, then we can say that 'P can give Q 12 points'.
Formulas
  • If P is n times as fast as Q and P gives Q a start of x meters, then the length of the race course, so that both P and Q reaches the winning post at the same time = xn/(n-1) meters.
  • If P can run x meters race in t1 seconds and Q in t2 seconds, where t1 < t2, then P beats Q by a distance of x(t2 – t1)/ t2 meters.
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