# Inverse proportion

In an inverse proportion, when one quantity increases by a certain factor, the other quantity decreases by the same factor.

A good real-life example of inverse proportion is the speed you drive and the time it takes to travel a certain distance. Suppose you need to drive to a city that is located 200 miles away.

The following table shows the time it will take you to get to your destination based on the speed.

 Speed (miles per hour) Time 20 m/h 10 hours 40 m/h 5 hours 80 m/h 2.5 hours

Did you make the following observations?

• 20 × 2 = 40  and  40  × 2 = 80
• 10 ÷ 2 = 5    and   5 ÷ 2 = 2.5

This means that every time you multiply the speed by 2, the time it takes is divided by 2 or multiplied by 1/2.

In general, with inverse proportion, when one quantity is multiplied by x, the other quantity is divided by x or multiplied by 1/x

Furthermore, notice the following:

20 × 10 = 200

40 × 5 = 200

80 × 2.5 = 200

200 is a constant, so let k = 200.

20, 40, or 80 is the independent variable, so let x = 20, 40, or 80

10, 5, or 2.5 is the dependent variable, so let y = 10, 5, or 2.5

We get  x × y = 200  or  y = 200/x

In general, with inverse proportion, y = k/x and we say that y is inversely proportional to x.

## Other real-life examples of inverse proportion

• The number of people doing something and the time it takes to do it. As the number of people increases, the time it takes to finish decreases.
• Sharing a specific amount of money with a certain amount of people. As the number of people increases, the amount decreases.
• Suppose your income is constant. The money you save is inversely proportional to your expenses.

Homepage

Inverse proportion

## Recent Articles 1. ### High School Math Teacher

Jan 20, 20 01:57 PM

Top-notch information for those who want to become a high school math teacher. All important stuff that you need to know before making a move can be found right here on this website.

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius! Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.