1. 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.
2. In this article, we will discuss an important concept of Time, Speed and Distance i.e. Races and Games. A race is a competition in which the competitors have to cover a given distance in the least time. A race may involve running, riding, driving, sailing, rowing etc.
3.
- Races: A contest of speed in running, riding, driving, sailing or rowing is called a race.
- Race Course: The ground or path on which contests are made is called a race course.
- Starting Point: The point from which a race begins is known as a starting point.
- Winning Point or Goal: The point set to bound a race is called a winning point or a goal.
- Winner: The person who first reaches the winning point is called a winner.
- Dead Heat Race: If all the persons contesting a race reach the goal exactly at the same time, the race is said to be dead heat race.
- Start: Suppose A and B are two contestants in a race. If before the start of the race, A is at the starting point and B is ahead of A by 12 metres, then we say that 'A gives B, a start of 12 metres'.
- 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 - 12) = 88 metres.
- In a 100 race, 'A can give B 12 m' or 'A can give B a start of 12 m' or 'A beats B by 12 m' means that while A runs 100 m, B runs (100 - 12) = 88 m.
- Games: 'A game of 100, means that the person among the contestants who scores 100 points first is the winner'.
- If A scores 100 points while B scores only 80 points, then we say that 'A can give B 20 points'.
