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 |

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!

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

3(50) = x60Solve 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**