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The time taken to paint a school varies inversely with the number of painters completing the task - HSC - SSCE Mathematics Standard - Question 9 - 2024 - Paper 1

Question 9

The time taken to paint a school varies inversely with the number of painters completing the task. It takes 6 painters a total of 20 days to paint a school. How ma... show full transcript

Worked Solution & Example Answer:The time taken to paint a school varies inversely with the number of painters completing the task - HSC - SSCE Mathematics Standard - Question 9 - 2024 - Paper 1

Step 1

Understanding Inverse Variation

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Answer

The time taken (T) varies inversely with the number of painters (P). This relationship can be expressed as:
$T imes P = k$
where k is a constant.

Step 2

Finding the Constant (k)

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Answer

Given that it takes 6 painters a total of 20 days:
$T = 20, P = 6$
Substituting these values into the equation:
$20 imes 6 = k$
Thus,
k = 120.

Step 3

Calculating Time for 15 Painters

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Answer

Now, we need to find the time taken (T) when there are 15 painters. Using the constant k found:
$T imes 15 = 120$
Solving for T:
$T = \frac{120}{15} = 8$
Therefore, it would take 15 painters 8 days to paint the school.

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