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Inverse Variation Formula
Inverse variation: A constant product
Inverse variation occurs when two variables have a constant product.
Formula for Invervse 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 |
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 varation are 2 and 4.
x + y = 3 is the equation of a line
and 4 is acutally an example of direct variation (as opposed to inverse variation) because the larger x gets the larger y gets!
practice 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.
Step 1) 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
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