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Inverse Variation Practice Problems

Multiply a known pair to get k = xy, then use y = k ÷ x. The word problems cover travel time, work crews, gas pressure and brightness.

  1. 1.

    varies inversely with , and when . What is ?

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    .

  2. 2.

    With , find when .

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    .

  3. 3.

    varies inversely with , and when . Find when .

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    , so .

  4. 4.

    A table shows = 1, 2, 5 and = 20, 10, 4. It is an inverse variation. What is ?

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    Every product is 20.

  5. 5.

    A trip takes 4 hours at 60 mph. How many hours does it take at 80 mph?

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    Distance , so hours.

  6. 6.

    A trip takes 5 hours at 48 mph. How many hours at 60 mph?

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    , so .

  7. 7.

    Eight workers build a fence in 9 days. How many days would 12 workers take?

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    worker-days, so .

  8. 8.

    Six painters finish a job in 10 days. How many days would 15 painters take?

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    painter-days, so .

  9. 9.

    At constant temperature, pressure varies inversely with volume. A gas at 2 atm fills 9 liters. What is the pressure at 6 liters, in atm?

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    , so atm.

  10. 10.

    Brightness varies inversely with the square of distance. A lamp gives 36 units at 2 m. How many units at 6 m?

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    , so .

  11. 11.

    varies inversely with the square of , and when . Find when .

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    , so .

  12. 12.

    varies inversely with , and when . Write the equation: ?

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    , so .
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Inverse Variation Practice Problems

These problems follow the inverse variation lesson. In every inverse variation the product stays the same.

The equation

Common mistakes to watch for

  • Writing . Inverse variation is : as one quantity doubles, the other halves.
  • Finding by dividing. For inverse variation, , the product, not the quotient.
  • Assuming any decreasing relationship is inverse. Check that stays constant; a line with negative slope is not inverse variation.
  • Forgetting powers. “Inversely with the square of ” means .

Frequently Asked Questions

How do I find the constant of inverse variation?+

Multiply a matching pair: k = x × y.

What is inverse square variation?+

y = k ÷ x², so k = y × x². Brightness and gravity behave this way with distance.

How do I type my answers?+

Type numbers without units, fractions like 5/3, and expressions like 2x + h. For intervals use parentheses or brackets and oo for infinity, for example (2, oo).

More practice problems

Direct Variation Practice Problems Rational Equations Practice Problems Work Rate Practice Problems