Races And Games

Important Formulas :

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 (or Goal) 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 competitors in a race. Lets examine some of the general statements and their mathematical interpretations.
Some 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.]

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 point at the same time =x(nn?1) metres

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 xt2(t2?t1) metres