The **inverse rule of three** allows you to calculate the quantity of one quantity corresponding to a given quantity of the other quantity inversely proportional to the first one. If the previous explanation did not help you much, hopefully this one will help you a little more.

It should **apply an inverse rule of three** when there is a relationship between the quantities as follows:

- A plus → minus.
- A minus → plus.

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## When is the inverse rule of three made?

As we have said before, **the inverse rule of three is applied when there is an inverse relationship of proportionality** between two variables. There are two possible cases:

- As one variable increases, the other decreases.
- As one magnitude decreases, the other increases.

As you can see, they are inversely proportional because they do not increase or decrease at the same time, but when one goes up, the other goes down and vice versa.

Remember that we also have a rule of three calculator normal for when there is a relationship of proportionality between the unknowns involved in the problem.

## How to make the inverse rule of three

Now that you know that you have to make an inverse rule of three when there is an inversely proportional relationship between two quantities, we are going to show you how to do it.

You simply have to **apply the following formula** mathematics:

What we are calculating is the amount of the variable 'y' that corresponds from the relationship we know of 'A' and 'B'. To make it clearer, let's see an exercise solved in the next point.

## Example of inverse rule of three

A pipe provides a flow rate of 18 liters of water every minute, taking 14 hours to fill a container. How long would it take to fill it if the pipe had a flow rate of 7 liters of water every minute?

Where is the inverse proportionality relationship? If you notice, as the water flow rate decreases, the filling time increases and, therefore, this problem must be solved by applying an inverse rule of three.

## Exercise solved

Let's see another exercise** The following is a typical elementary school or ESO (Secondary School) problem in which we will have to apply an inverse rule of three**. The problem statement reads as follows:

3 people build a house in 12 hours, how long will it take to build it if 9 people collaborate?

**The first step of all is to identify the inverse proportional relationship.** to know if we have to apply the inverse rule of 3. As you can deduce, if the number of people building the house increases, it is logical that the time needed to finish it will decrease.

Therefore,** we already know that we have to use the inverse rule of 3** to solve this problem. Now we go to the formula from before and we are left with:

3 persons → 12 hours

9 persons → and

We solve to find out how much y is worth:

y = (3 persons x 12 hours) / 9 persons = 4 hours

If you have any questions or are having problems with **solving an exercise related to the inverse rule of three**Leave us a comment and we will help you as soon as possible.