Question

How many workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days?

Answer 1

Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

Inversely proportional relationship

Two variables are related when a change in one of them causes a change in the other.

Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.

In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.

Simple inverse rule of three

The simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.

To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:

A → B

C → X

So: $X=\frac{AxB}{C}$

Amount of workers needed

The number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:

9 days → 8 workers

6 days → amount of workers

So:$amount of workers=\frac{9 daysx8 workers}{6 days}$

amount of workers= 12 workers

Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.

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