Math Lesson 4.3.5 - Inverse (Indirect) Proportion

[ 1 Votes ]

Welcome to our Math lesson on Inverse (Indirect) Proportion, this is the fifth lesson of our suite of math lessons covering the topic of Proportion, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Inverse (Indirect) Proportion

This type of proportion occurs when the quantities involved change inversely, i.e. when one of them increases by a certain factor, the other quantity decreases by the same factor. For example, if 20 people can do a job in 5 days, it takes 50 days to 2 workers to complete the same job. This is because decreasing the number of workers increases by the same factor the time necessary to complete the work.

By definition, inverse (or indirect) proportion occurs when a decrease in one quantity or variable causes an increase by the same factor in another quantity or variable.

If we continue operating with the symbols of direct proportion, we can express an inverse proportion as

a:b = d:c


a/b = d/c

Example 5

A car travelling at 60 km/h reaches the destination in 3 hours. How long does it take to this same car to reach the same destination if it travels at 20 km/h?

Solution 5

From Physics, it is known that distance = speed × time. Since the distance is the same (there is the same destination), this is a typical situation involving two quantities related to each other in an inversely proportional way, because any decrease in speed brings an increase in travelling time by the same factor. Thus, we have for the two situations given in the clues:

Reference speed × Reference time = Actual speed × Actual time


v1 × t1 = v2 × t2

We can write the last equation in proportion form using fractions, i.e.

v1/v2 = t2/t1

where v1 = 60 km/h, t1 = 3 h, v2 = 20 km/h and t2 is to be calculated. Thus, we have:

60 km/h/20 km/h = t2/3 h

Using the cross product method described earlier, we obtain

60 × 3 = 20 × t2
t2 = 60 × 3/20
= 9 h

More Proportion Lessons and Learning Resources

Ratio and Proportion Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Lesson IDMath Lesson TitleLessonVideo
4.3.1Definition of Proportion
4.3.2Direct Proportion
4.3.3Graph of Direct Proportion
4.3.4Cross Product in Direct Proportion
4.3.5Inverse (Indirect) Proportion
4.3.6Graph of Inverse Proportion

Whats next?

Enjoy the "Inverse (Indirect) Proportion" math lesson? People who liked the "Proportion lesson found the following resources useful:

  1. Inverse Feedback. Helps other - Leave a rating for this inverse (see below)
  2. Ratio and Proportion Math tutorial: Proportion. Read the Proportion math tutorial and build your math knowledge of Ratio and Proportion
  3. Ratio and Proportion Video tutorial: Proportion. Watch or listen to the Proportion video tutorial, a useful way to help you revise when travelling to and from school/college
  4. Ratio and Proportion Revision Notes: Proportion. Print the notes so you can revise the key points covered in the math tutorial for Proportion
  5. Ratio and Proportion Practice Questions: Proportion. Test and improve your knowledge of Proportion with example questins and answers
  6. Check your calculations for Ratio and Proportion questions with our excellent Ratio and Proportion calculators which contain full equations and calculations clearly displayed line by line. See the Ratio and Proportion Calculators by iCalculator™ below.
  7. Continuing learning ratio and proportion - read our next math tutorial: Properties of Proportion. Geometric Mean

Help others Learning Math just like you

[ 1 Votes ]

We hope you found this Math tutorial "Proportion" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.

Ratio and Proportion Calculators by iCalculator™