Practice Inverse Variation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A relationship where y = \frac{k}{x}: as one quantity doubles, the other halves—their product stays constant.

More workers means less time: if 4 workers take 6 hours, 8 workers take 3 hours.

Example 1

medium
\(y\) varies inversely with \(x\), and \(y = 8\) when \(x = 3\). Find \(k\) and the equation. Then find \(y\) when \(x = 6\).

Example 2

hard
Speed and travel time are inversely proportional for a fixed distance. At 60 km/h the trip takes 4 hours. How long at 80 km/h? Identify \(k\).

Example 3

medium
If \(y = k/x\) and \(y = 12\) when \(x = 5\), find \(y\) when \(x = 15\).

Example 4

hard
The pressure \(P\) and volume \(V\) of a gas at constant temperature satisfy \(PV = k\). If \(P = 4\) atm when \(V = 6\) L, find \(P\) when \(V = 8\) L.
← Back to Inverse Variation Worked Examples Formula Explained