Introduction to Races and Games

Races:

Starting Point: The point from which the race begins is the starting point.

Winning Point (or Goal): The point where the race ends is the winning point or goal.

Dead Heat: If all the contestants in a race reach the ending point at exactly the same time, then the race is said to end in dead heat.

In a race between 2 contestants A and B,

  • If A gives B a start of ‘x’ metres, then A is at the starting point and B is ahead of A by ‘x’ metres.
  • If A beats B by ‘x’ metres, say, in a 100m race, then while A runs 100 metres B runs 100-x metres.
  • If A gives B a start of ‘t’ seconds, then A starts ‘t’ seconds after B starts from the same starting point.
  • If A beats B by ‘t’ seconds, then A finishes the race ‘t’ seconds before B

Note : From the above points we see that, for a race of 100 metres the following statements are equivalent – “A beats B by 10 metres” or “A gives B a start of 10 metres’ or “A can give B a start of 10 metres”

Games:

In a game of 100, if A scores 100 points first, then A is the winner.

In a game of 100, If A gives B 10 points, it implies that when A scores 100 points, B scores 90 points.