Six people can finish a wall in 8 hours. If only 4 people are available, how many hours do they have to work to finish the same job? TYPE OF PROPORTION: _________________________ FINAL ANSWER:

In Mathematics, Proportion is a statement of equality between two ratios. It has three types namely DIrect Proportion, Indirect Proportion, and Partitive Proportion.

It is Direct Proportion if:

As one term increases, the other term increases at the same rate.
As one term decreases, the other term decreases at the same rate.

It is Indirect Proportion if:

As one term increases, the other term decreases proportionately.
As one term decreases, the other term increases proportionately.

It is Partitive Proportion if:

A value is divided into parts proportionately to the given ratio.

For this particular problem, six people can finish a wall in 8 hours. If only four people are available, how many hours do they have to work to finish the same job?

This is an example of Indirect Proportion because the greater the amount of workers, the shorter the amount of time it would take them to finish the job. In the same manner, the lesser the amount of workers, the longer the amount of time it would take them to finish the job.

To put it simply, the terms in this problem are inverted, making it an Indirect Proportion.

To solve for Indirect Proportion, make use of the following formula:

[tex] \frac{term \: with \: greater \: value}{term \: with \: lesser \: value} = \frac{term \: with \: longer \: value}{term \: with \: shorter \: value} [/tex]

Let x represent the missing value:

[tex] \frac{6 \: people}{4 \: people} = \frac{x}{8 \: hours} [/tex]

Then, cross multiply.

[tex]4x = 48[/tex]

Divide both sides by 4.

[tex]x = 12[/tex]

If there are only 4 people available for the job, it would take them 12 hours to finish.

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