Inverse Variation Formula

Inverse variation: A constant product

Inverse variation occurs when two variables have a constant product.

Formula for Inverse Variation

Inverse variation occurs when two variables such as XY are always equation to some constant K.

Example of Inverse Variation XY = 100

The effect of this relationship is that when one variable decreases the other variable increases as summarized in the table below

X Y XY
1 100 100
2 50 100
4 25 100
5 20 100
10 10 100
20 5 100
25 4 100
50 2 100
100 1 100
Problem 1

Identify which equations below represent inverse variation.

If you compare each equation with the formula for inverse variation, the only two that are not inverse variation are 2 and 4.

x + y = 3 is the equation of a line and 4 is a cut ally an example of direct variation (as opposed to inverse variation) because the larger x gets the larger y gets!

Problem 2

The speed of a laundry truck varies inversely with the time it takes to reach its destination. If the truck takes 3 hours to reach its destination traveling at a constant speed of 50 miles per hour, how long will it take to reach the same location when it travels at a constant speed of 60 miles per hour?

Set up the equation. Since this is an inverse variation relationship know that speed × time equals a constant.

3(50) = x60

Solve the equation that you set up in step 1

  • 3(50) = x60
  • 150 = x60
  • 150 ÷ 60 = x
  • 2.5= x
The answer is 2.5 hours