Question

The time to complete a building project is inversely proportional to the number of people working on the job it takes 30 days for 6 workers to complete the job. If they need to complete the job in 20 days, how many workers will they need?

Answer 1

Answer:

$4$

Step-by-step explanation:

if 30days =6workers

20days =?

$= \frac{20 \times 6}{30} \\ = 4$

Answer 2

Proportions can be inverse, direct, joint or combined.

They need 9 workers to complete the job in 20 days

Represent time with t, and the workers with w.

So, the proportional relationship is:

$t\ \alpha\ \frac 1w$

Express as an equation

$t\ =\ \frac kw$

Where k represents the proportionality constant

Make k the subject

$k =wt$

6 workers complete the job in 30 days.

This means that: w =6, and t =30

So, we have:

$k =6 \times 30$

$k =180$

Substitute 180 for k in $k =wt$

$180 = wt$

In 20 days. we have:

$180 = w \times 20$

Divide both sides by 20

$9 = w$

Rewrite as:

$w = 9$

Hence, they need 9 workers to complete the job in 20 days

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