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The time taken to clean a warehouse varies inversely with the number of cleaners employed - HSC - SSCE Mathematics Standard - Question 13 - 2021 - Paper 1

Question 13

The time taken to clean a warehouse varies inversely with the number of cleaners employed. It takes 8 cleaners 60 hours to clean a warehouse. Working at the same r... show full transcript

Worked Solution & Example Answer:The time taken to clean a warehouse varies inversely with the number of cleaners employed - HSC - SSCE Mathematics Standard - Question 13 - 2021 - Paper 1

Step 1

Determine the relationship

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Answer

Given that the time taken to clean a warehouse varies inversely with the number of cleaners, we can express this relationship mathematically as:

$T = \frac{k}{N}$

where:

$T$ is the time taken,
$N$ is the number of cleaners, and
$k$ is a constant.

Step 2

Find constant k

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Answer

Using the information provided, when 8 cleaners are employed, it takes 60 hours to clean the warehouse:

$60 = \frac{k}{8}$

To find $k$ , we can rearrange this equation:

$k = 60 \times 8 = 480.$

Step 3

Calculate time with 10 cleaners

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Answer

Now, we want to find out how long it will take 10 cleaners. Using the same formula:

$T = \frac{480}{10} = 48.$

Therefore, it would take 10 cleaners 48 hours to clean the same warehouse.

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