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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.

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 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?

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

v_{1} × t_{1} = v_{2} × t_{2}

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

where v_{1} = 60 km/h, t_{1} = 3 h, v_{2} = 20 km/h and t_{2} is to be calculated. Thus, we have:

Using the cross product method described earlier, we obtain

60 × 3 = 20 × t_{2}

t_{2} = *60 × 3**/**20*

= 9 h

t

= 9 h

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

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

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