Inverse Variation: Definition, Equation & Examples

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  • 0:00 Real Life Examples
  • 1:37 Definition
  • 2:00 Equations, Tables, Graphs
  • 2:55 Other Life Examples
  • 3:19 Lesson Summary
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Lesson Transcript
Instructor: Sharon Linde
Have you heard of an inverse variation? Don't worry, most people haven't, but it's really quite simple. If you've ever ridden a bike, you've seen inverse variations in action. This lesson will fill you in - read on for details.

Real-Life Examples

Before getting into the nitty gritty of inverse variation, let's see an example in real life that's easy to relate to. If you think about riding a bike, you can easily figure out that the time it takes you to cover a specific distance varies inversely with the speed. If you go really fast, it takes you a lot less time than if you go really slow.

Let's say you and a friend decide to go on a 20 mile bike ride. Your friend asks, 'Do you think we can finish in under two hours?' You're experienced in biking and know that you can average 20 miles an hour. 20 miles divided by 20 miles per hour is 1 hour, which is definitely under 2 hours. You answer, 'I certainly hope so! If we aren't done in under 2 hours, I need to pick a different sport.'

However, when you show up the next day and see your friend's bike you start having second thoughts. His bike is old and rusty. The way he strains when he lifts it out of the car, it looks like it weighs twice what yours does. 'What is that thing?' you ask your friend.

'What? This is my bike. I know it's not as nice as yours, but it will still do the job.'

You're skeptical but you start on your bike ride anyway. The going is very slow, because your friend on his terrible old bike can only average about 10 miles an hour. It takes the two of you the full 2 hours to complete the ride because the speed you travel and the time it takes you to cover a set distance vary inversely.

The equation for this scenario is:

rate x time = distance, or time = distance / rate.


This bike riding scenario represents an inverse variation. There are several of ways to think about inverse variations, but let's start with the definition and go from there. An inverse variation is when two variables can be expressed by an equation where the product equals a constant. Sound complicated? Don't worry, it's pretty simple. Let's take a look.

Equations, Tables, Graphs

If we translate the definition into the language of mathematics, we get an equation that looks like this:

xy = k (where k is a constant not equal to 0)

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