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
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
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.