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At its core, quantitative aptitude involves the ability to understand and solve problems involving numerical and logical reasoning. It's a pillar of competitive exams and aptitude tests, where understanding concepts like speed, time, and distance is essential. In our example, we applied quantitative aptitude to determine a person's typical speed by setting up an equation using given information.

To excel in quantitative aptitude, especially in speed-time-distance problems, students must be adept at creating relationships between these entities and forming equations that represent real-world scenarios. Using algebra as a tool, solving for unknown variables becomes a straightforward process of manipulating these equations.

Algebraic equations are fundamental tools used to represent problems where you seek to determine unknown quantities. In the context of the given exercise, we used an algebraic equation, specifically a linear equation in two variables, to represent the relationship between Deepesh's speed (\(s\text{ km/h}\)) and the time (\(t\text{ hours}\)) taken to cover a distance of 600 km.

An equation like \(s \times t = 600\) offers a clear, concise way to show that Deepesh’s speed multiplied by the time he travels equals the distance. Mastering the use of these equations is crucial to solving many real-world problems efficiently. Algebra trains the mind to think logically and to approach complex problems in a structured manner, breaking them down into smaller, more manageable parts.

A system of equations consists of two or more equations with the same set of unknowns. In our speed-time-distance problem, we had two linear equations constituting a system. Solving a system of equations like this usually involves finding a common variable to eliminate or substitute, allowing you to isolate the remaining variable.

The exercise demonstrates the substitution method, where one equation is solved for a particular variable, which is then inserted into the other equation. For instance, \(s \times t = 600\) and \( (s + 20) \times (t - 1) = 600\) are two equations that form our system. Solving for one variable (\(t\text{, in this case}\) and plugging it into the second equation simplifies the problem to having one unknown (\(s\text{, in this case}\). Systems of equations are not limited to two variables and can involve multiple variables and equations, requiring different methods like elimination, substitution, or matrix operations to solve.