### 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.

**5. Dead-heat Race**

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.