# Math Lesson 4.3.5 - Inverse (Indirect) Proportion

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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

or

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

or

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
Tutorial
Revision
Notes
Revision
Questions
4.3Proportion
Lesson IDMath Lesson TitleLessonVideo
Lesson
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

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7. Continuing learning ratio and proportion - read our next math tutorial: Properties of Proportion. Geometric Mean

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