Abigail and Mary are tracking the number of steps they walk. Abigail records that she can walk 6000 steps in 50 minutes. Mary writes the equation = 118, where is the number of steps and is the number of minutes she walks, to describe her step rate. This week, Abigail and Mary each walk for a total of 5 hours. Who walks more steps? How many more?

Answer:

Abigail walks more steps than Mary.

To find out who many steps each one of them walks in a week, we have to carry out different calculations starting with Abigail.

                Calculation for number of steps taken by Abigail

Abigail takes 6000 steps in 50 minutes. We can use this information to scale up his number of steps over a period of 5 hours(300 minutes.). The quickest way to do this calculation, is to notice that there are 6 different 50 minute segments in 300 minutes. This means that the number of steps taken in 5 hours is  steps.

Another way to do this calculations is to use proportions

.

Abigail takes 36000 steps that week.

                Calculation for number of steps taken by Mary

The number of steps taken by Mary is given by the is given by the function  where  is the time in minutes. Mary walks for a total of 5 hours or 300 minutes. We calculate the number of steps she takes as shown below,

Mary takes a total of 35400 steps.

Since  36000 steps is greater than 35400 steps, we conclude that Abigail walks more steps than Mary.

Is the graph above proportional or non-proportional?

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