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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

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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 clean... 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 Total Working Hours

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Answer

To determine how long it took the 5 cleaners yesterday, we convert 4 \frac{1}{2} hours into an improper fraction:

412=92 hours4 \frac{1}{2} = \frac{9}{2} \text{ hours}

Thus, the total work done in cleaner hours is:

5 cleaners×92 hours=452 cleaner hours=22.5 cleaner hours5 \text{ cleaners} \times \frac{9}{2} \text{ hours} = \frac{45}{2} \text{ cleaner hours} = 22.5 \text{ cleaner hours}

Step 2

Determine Cleaner Hours for Today

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Answer

Today, there are 3 cleaners, so we need to find out how many hours they will work to clean the same amount of rooms:

Let ( x ) be the number of hours each cleaner works today. Thus, we have:

3x=22.53x = 22.5

Solving for ( x ):

x=22.53=7.5 hoursx = \frac{22.5}{3} = 7.5 \text{ hours}

Step 3

Calculate Payment per Cleaner

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Answer

Each cleaner is paid £8.20 for each hour or part of an hour worked:

Total payment for each cleaner today is:

7.5 hours×£8.20=£61.507.5 \text{ hours} \times £8.20 = £61.50

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