Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 1 • Question 10

A new supermarket needs to stack all the items on the shelves. It will take 3 workers, each working 4 hours a day, 5 days to complete. The supermarket decides to get 5 workers, each working 3 hours a day. Assume that each worker works at the same rate. a) How many days will it take to stack the shelves? You must show your working. b) How does the assumption affect your answer to part a).

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Video Transcript

A new supermarket needs to stack all the items on the shelves. It will take three workers, each working four hours a day, five days to complete. The supermarket decides to get five workers, each working three hours a day. Assume that each worker works at the same rate. Part a) How many days will it take to stack the shelves? You must show your working.

There is also a part b) that we will look at later. In the example, we were told that three workers work for four hours a day. Three multiplied by four is equal to 12. This means that these three workers work a total of 12 hours a day of work between them. We were told that it would take these three workers five days to complete the job. Five multiplied by 12 is equal to 60. This means that we have a total of 60 hours work over the five days. We can therefore say that it will take 60 hours of work to stack all the items on the shelves in the new supermarket.

The supermarket decided to employ five workers to complete this work. 60 divided by five is equal to 12. This means that the workers need to work for 12 hours each. We were also told that these five workers were employed for three hours per day. They need to work for a total of 12 hours and on each day they can work for three hours. Therefore, we need to divide 12 by three. This is equal to four. Assuming that each worker works at the same rate, then it will take four days to stack the shelves.

An alternative method to solve this problem would be to set up an equation. The total time to complete the job can be calculated by multiplying the number of workers by the amount of time worked per day by the number of days. In the example, there were three workers working four hours per day and it took five days to complete. Therefore, we can multiply three by four by five.

The supermarket actually employed five workers working three hours per day and we needed to calculate how many days it would take. Let’s call this 𝑥. Using the same equation workers multiplied by time multiplied by days gives us five multiplied by three multiplied by 𝑥. We could multiply out these calculations.

However, you might notice that we have a three and a five on both sides of the equation. This means that we can divide both sides of the equation by three and also by five. When we do this, we are left with four is equal to 𝑥. Once again, we have proved that the number of days it will take to stack the shelves is four.

Part b) of the question said the following. How does the assumption affect your answer to part a)?

We were told to assume that each worker works at the same rate. In reality, one of two things could happen: either some of the workers work at a slower rate or they work at a quicker rate. If some of the workers work at a slower rate, it will take longer to complete the task, whereas if some of the workers work at a faster rate, it will take less time to complete the task. Either way, if we don’t make the assumption, the number of days could increase or decrease.

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