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 : 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.
Showing a random 20 of 50 problems.
Example 1
mediumA loud speaker's perceived loudness varies inversely with the square of distance. If it is at m, find loudness at m.
Example 2
medium. If is multiplied by , by what factor does change?
Example 3
medium varies inversely with , and when . Find and the equation. Then find when .
Example 4
easyCan in the inverse variation ?
Example 5
mediumA test pilot finds time-to-cover km varies inversely with average speed. At km/h it takes s. Find time at km/h.
Example 6
mediumIf varies inversely with and when , find when .
Example 7
easy varies inversely with , and when . Find when .
Example 8
medium varies inversely with . Given two pairs and , find .
Example 9
easyDoes the equation describe an inverse variation?
Example 10
challenge passes through and . Find .
Example 11
hardThe pressure and volume of a gas at constant temperature satisfy . If atm when L, find when L.
Example 12
challenge varies inversely with . When increases by , decreases by how many percent?
Example 13
easyIn , if triples, what happens to ?
Example 14
challenge varies inversely with . If values at and differ by , find .
Example 15
challengeQuantities satisfy . If and are positive integers and , how many ordered pairs exist?
Example 16
easyIf varies inversely with and when , find .
Example 17
mediumIt takes pipes hours to fill a tank. How many pipes fill it in hours?
Example 18
medium varies inversely with . When , . Find when .
Example 19
easyIn , what happens to when doubles?
Example 20
mediumA trip takes hours at mph. How fast must you drive to make it in hours?