Inverse Variation

Inverse variation describes a relationship between two quantities where, as one quantity increases, the other decreases, and vice versa. Importantly, their product remains constant.

Think of it like a seesaw: when one side goes up, the other goes down.

The following diagram shows the key concepts of inverse variation. Scroll down the page for more examples and solutions on Inverse Variation Word Problems.

 

Algebra Word Problem
Steps to Solve Inverse Variation Word Problems

1. Identify the Variables: Determine which quantities are related and assign variables to them (e.g., y and x).
2. Write the Inverse Variation Equation: Use the formula y = k/x or y × x = k.
3. Find the Constant of Variation (k): Use the given values of y and x to solve for k.
4. Rewrite the Equation with k: Substitute the value of k into the equation y = k/x
5. Solve for the Unknown: Use the equation to find the unknown value of y or x.

Inverse Variation
Real life examples of inverse variation

1. The time a trip takes and the speed traveled.
2. The time taken to spread landscaping rock and the number of people working.
3. The amount of money needed per person for gasoline and the number of people in the car.

Example:

1. Y varies inversely as x. Y = 4 when x = 2.
2. The time t requires to empty a tank varies inversely as the rate r of pumping. If a pump can empty a tank in 2.5 hours at a rate of 400 gallons per minute, how long will it take to empty a tank at 500 gallons per minute?
3. The force F needed to break a board varies inversely with the length l of the board. If it takes 24 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 5 feet long?
4. Y varies inversely as the square root of x. Y = 6 when x = 16. Determine the inverse variation equation. Then determine y when x = 4.

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Inverse Variation Application
When modeling real world situations, we often use what’s called inverse variation to describe a relation between two variables. Inverse variation is a relation in which the absolute value of one variable gets smaller while the other gets larger. Inverse variation and direct variation are important concepts to understand when learning equations and interpreting graphs.

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Math Variation: Direct and Indirect
When modeling real world situations, we often use what’s called inverse or indirect variation to describe a relation between two variables. Indirect variation is a relation in which the absolute value of one variable gets smaller while the other gets larger. Indirect variation and direct variation are important concepts to understand when learning equations and interpreting graphs.

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What’s the Inverse Variation or Indirect Proportionality Formula?
Ever heard of two things being inversely proportional? Well, a good example is speed and time. The bigger your speed, the less time it takes to get to where you are going. So when one variable is big, the other is small, and that’s the idea of inverse proportionality. But you can express inverse proportionality using equations, and that’s an important thing to do in algebra.

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Check out many other Algebra Word Problems
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