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Yesterday it took 5 cleaners 4 \frac{1}{2} hours to clean all the rooms in a hotel - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2

Question 9

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Yesterday it took 5 cleaners 4 \frac{1}{2} hours to clean all the rooms in a hotel. There are only 3 cleaners to clean all the rooms in the hotel today. Each cleaner... show full transcript

Worked Solution & Example Answer:Yesterday it took 5 cleaners 4 \frac{1}{2} hours to clean all the rooms in a hotel - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2

Step 1

Calculate Time Taken for Today

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Answer

First, we need to determine how many hours it took for 5 cleaners to clean the hotel. The total time was 4.5 hours. To find the time for 3 cleaners, we use the concept of inverse proportionality, where more cleaners mean less time.

Let the total time taken today be represented by ( t ).

Using the formula:

$5 \times 4.5 = 3 \times t$

We can solve for ( t ):

$t = \frac{5 \times 4.5}{3} = 7.5 \text{ hours}$

Step 2

Determine Pay for Each Cleaner

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Answer

Now, we calculate how much each cleaner will be paid for their work today. Since each cleaner is paid £8.20 for each hour or part of an hour, we can use the following calculation:

$\text{Payment} = 7.5 \text{ hours} \times £8.20 = £61.50$

Thus, each cleaner will be paid £61.50 today.

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