# Inverse Variation

In this video, we are going to apply inverse variation.

First, let’s discuss direct variation. It is basically proportions.

For example:
The number of gallons of gasoline is proportion to the number of miles.
$\frac{mile}{gallon}=\frac{20 miles}{1 gallon}=\frac{40 miles}{2 gallons}$

Inverse variation is the opposite of direct variation, where the increase of one meets the decrease of the other.

For example:
If it takes 2 hours for a 5-pound block of ice to melt in a 60-degree Fahrenheit room, how long will it take a 5-pound of ice to melt in an 80-degree Fahrenheit room, assuming time and temperature are inversely related.

First, let’s use the equation t1T1=t2T2 where t is time, T is temperature

Substitute the values
$(2)(60)=t(80)$

Multiply
$120=80t$

Divide 80 from both sides to isolate x
$1.5=t$
So it takes 1.5 hour for the ice to melt

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