Inverse Variation
Inverse variation occurs when an increase in one variable causes a balanced decrease in another variable.
Fundamental Principles
Inverse Variation (Y ∝ 1/X)
A relationship where the product of two variables is always equal to a constant value. This is written as x * y = k, where 'k' is the constant of variation.
Essential Formulation Tips
- When two values change by inverse variation, set up your calculation using a balanced product: x1 * y1 = x2 * y2.
- Classic real-world examples include speed and travel time (faster speed means less travel time) or workforce size and project duration.
Shortcut Execution Techniques
- If the number of workers is doubled, the time required to finish the project is cut exactly in half, because their product must equal the same constant value.
Contextual Inquiries (FAQs)
Q: What does an inverse variation look like on a graph?
A: It forms a curve called a hyperbola, which approaches the axes but never touches them.
Example Breakdown: Calculating Worker Dynamics
Standard inverse work-rate application.Identify the inverse variation relationship: Workers * Days = Constant Total Effort.
Set up the balanced equation: x1 * y1 = x2 * y2 -> 10 * 6 = 12 * y2.
Multiply the values: 60 = 12 * y2.
Divide to solve for y2: y2 = 60 / 12 = 5 days.
Inverse Variation Problems
Practice solving speed, time, and worker resource problems using product balance rules.
Q1. A car travelling at 60 mph reaches its destination in 3 hours. How long will the trip take at 45 mph?