Problem 42 - College Algebra

Question

What does it mean if two quantities vary inversely?

Step-by-Step Solution

Answer

Inverse variation is a relationship where the product of the two variables is always constant. When one variable increases, the other decreases proportionally, and vice versa. For instance, the relationship between speed and time while travelling.

Step 1: Understand Inverse Variation

Inverse variation describes a relationship between two variables in which the product is a constant. When one variable increases the other variable decreases in proportion so that the product of the two variables remains unchanged.

Step 2: Mathematical Representation of Inverse Variation

If two quantities \(x\) and \(y\) that are in inverse variation, it could be algebraically expressed as \(xy = k\) where \(k\) is the constant. This means, if \(x\) increases, \(y\) has to decrease to keep \(k\) the same, and vice versa.

Step 3: Provide an Example

For example, consider the time and speed at which you travel. If you drive very fast, it will take you less time to go a certain distance. But if you drive slowly, it will take more time. So here, speed and time have an inverse relationship.