These lessons, with videos, examples and step-by-step solutions, help Algebra students learn how to solve inverse variation or inverse proportion problems and applications.

**Related Pages**

Direct Variation

Joint Variation

More Lessons for Grade 9 Math

Math Worksheets

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

**Algebra Word Problem**

Inverse Variation

Real life examples of inverse variation

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

**Example:**

- Y varies inversely as x. Y = 4 when x = 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?
- 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?
- 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.

**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.

**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.

**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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