### Races and Games

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## Races & Games

Races & Games
1. Race
A race is a contest of speed in running, riding, driving, sailing, rowing etc over a particular distance.

2. Race Course
Race course is the ground or path on which contests are conducted.

3. Starting Point
Starting Point is the point from which a race starts.

4. Winning Point (or Goal)
Winning Point is the point where a race finishes.

A race is said to be a dead-heat race if all the persons contesting the race reach the winning point (goal) exactly at the same time.

6. Winner
Winner is the person who first reaches the winning point.

7. Let A and B be two contestants in a race. Lets examine some of the general statements and their mathematical interpretations.
* A beats B by t seconds → A finishes the race t seconds before B finishes.
* A gives B a start of t seconds→ A starts t seconds after B starts from the same starting point.
* A gives B a start of x metres → While A starts from the starting point, B starts x meters ahead from the same starting point at the same time.
To cover a race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 - x) metres.
* Game of 100 → A game in which the participant who scores 100 points first wins.
* In a game of 100, A can give B 20 points → While A scores 100 points, B scores only 100-20=80 points.

8. If A is n times as fast as B and A gives B a start of x meters, then the length of the race course , so that A and B reaches the winning post at the same time
x *
n - 1
n
meters

9. If A can run x metre race in t1 seconds and B in t2 seconds, where t1 < t2, then A beats B by a distance

t2
x2
* (t2 - t1)meters.