Races and Games Concepts

Understanding the Concepts of Races and Games

Races is a sub-concept of time, speed, and distance, and most racing problems can be handled by understanding these two concepts.

First and foremost, we must have a fundamental conceptual knowledge of the relationship between Time, Speed, and Distance.

Speed = Distance / Time.

Second, in order to solve problems faster, we must comprehend the concept of proportionality between these terms.

1. Direct Proportion

The term 'direct proportion' refers to the direct link between two quantities. When one quantity rises, the other rises as well, and vice versa. As a result, a direct proportion is expressed as y ∝ x.

For Example

When the speed of a car is raised, it travels a greater distance in a given amount of time.

• Time & Distance are directly proportional
• Speed & Distance are directly proportional

2. Inverse Proportion

Inverse proportion explains the connection between two quantities in which one rises while the other falls and vice versa. As a result, an inverse proportion is expressed as y ∝ 1/x.

For Example

If the speed of a vehicle is increased, it will cover a fixed distance in less time.

• Time & Speed are Inversely proportional

By presenting an example, we will have a better understanding of these problems.

Example Problem

A can defeat B by 25 metres in a 100-metre race, while B can beat C by 4 metres. A can beat C in the same race by:

Solution:

This problem is commonly addressed using ratio concepts; from the provided data, we can deduce that after A completes the race, B covers 75 metres; this may be expressed as

A : B = 100 : 75 —----------- Equation 1

Conversely, we can deduce from the data that when B completes the race, C covers 96 m, which may be written as,

B : C = 100 : 96. —----------- Equation 2

When we combine these two equations, we obtain,

A: B: C = 100: 75: 72

So A beats C by (100 - 72) m = 28 m.