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Roots of a Number Money Tangent Line to a Circle, Normal Line Volume of a Cone Factoring Multiplying Fractions & Mixed Fractions Adding/Subtracting FractionsInverse Proportion is a similar idea to ** direct
proportion**, but slightly different.

With direct proportion shown on the direct proportion page, each part of a ratio increased at the same rate.

Such as the ratio examples below.

With inverse proportion however, one part of a ratio increases, as one part decreases.

For example, if you are climbing a mountain.

As the altitude increases and you get higher, the temperature will go down.

The height goes up, as the temperature goes down.

Temperature

On a journey, a car drives at a steady speed of **40**mph.

The journey eventually takes **3** hours, how much shorter in time would this journey have been
at a speed of **60**mph?

Speed

If the car was travelling at only 1mph, 40 times slower, then the journey time will be 40 times
longer.

As speed decreases , journey time increases.

(

Left part of ratio was divided by **40**, right side multiplied by **40**.

As the values are inversely related.

From here, we can multiply **1mph** by **60**, while also dividing **120hrs** by **60**.

This will give us the journey time for a speed of **60mph**.

The journey would take **2** hours at a speed of **60mph**,

which is **1** hour shorter than the journey time at **40mph**.

Like in the case of Direct Proportion, situations where the values are Inversely Proportional can
also be modeled with a formula. Such as the situation in example (2.1).

Where as the Speed went up , the Time taken went down.

It can be written that **S** ∝ \\boldsymbol{\\frac{1}{T}}
,

meaning that **S** is Inversely Proportional to ** T**.

To get a general inverse proportion formula for this situation, we start off by setting the proportion symbol to an equals sign, and replacing

Like in the case of direct proportion, here *k* is again a
constant, and again called the "constant of proportionality".

In a given ratio, two corresponding values of **S** and ** T** can be used to
establish the value

In example (2.1), when

Which results in the formula for the direct proportion in example (2.1):

So if you wanted to know what speed to travel at for the journey to take **4** hours.

A speed of **30mph** would result in a journey time of **4** hours.

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