Inverse proportion occurs when one quantity increases while the other decreases at the same rate. In simpler terms, when two values are inversely proportional, their product remains constant. This relationship can be written mathematically as:

\[

x \times y = k

\]

Where:

\(x\) and \(y\) are the two quantities,

\(k\) is the constant of proportionality.

As \(x\) increases, \(y\) decreases, and vice versa.

#### Example 1

Let’s say you are driving a car and want to calculate the relationship between speed and travel time. If you double your speed, the time to cover the same distance will be halved. This is an example of inverse proportion.

At 60 mph, the travel time for a certain distance is 2 hours.

If you increase your speed to 120 mph, the travel time becomes 1 hour.

Here, speed (\(x\)) and time (\(y\)) are inversely proportional:

\[

60 \times 2 = 120 \times 1 = 120 \, (constant)

\]

#### Example 2:

Suppose a project requires 5 workers and takes 8 days to complete. If you increase the number of workers to 10, how long will it take to complete the project?

Let \(x = 5\) workers and \(y = 8\) days.

We need to find \(y\) when \(x = 10\).

#### Using the inverse proportion formula

\[

x_1 \times y_1 = x_2 \times y_2

\]

\[

5 \times 8 = 10 \times y_2

\]

\[

40 = 10 \times y_2

\]

\[

y_2 = 4 \, \text{days}

\]

With double the workers, the project will take 4 days.

#### Using an Inverse Proportion Calculator

An Inverse Proportion Calculator can simplify solving problems like these. Simply input the known values, and the calculator quickly computes the unknown variable, making it ideal for students or professionals who need to solve inverse proportion problems accurately and efficiently.