Andrew and Sarah are tracking the number of steps they walk. Andrew records that he can walk 6000 steps in 50 minutes. Sarah writes the equation y=118x where y is the number of steps and x is the number of minutes she walks, to describe her step rate.

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

Solution:

Given:

Andrew walks 6000 steps in 50 minutes.

Number of steps Sarah walks is given by the equation :

[tex]y=118x[/tex]

where [tex]y[/tex] is the number of steps and [tex]x[/tex] is the number of minutes she walks.

Finding the number of steps each walks in 5 hours.

Total number of minutes in 5 hours = [tex]5\times 60 = 300\ min[/tex]

For Andrew:

Using unitary method:

If in 50 minutes Andrew walks = 6000 steps.

In 1 minute he will walk = [tex]\frac{6000}{50}[/tex] = 120 steps

In 300 minutes he will walk = [tex]120\times 300 = 36000[/tex] steps

Thus, Andrew will walk 36,000 steps in 5 hours.

For Sarah:

We will plugin [tex]x=300[/tex] in the equation and solve for [tex]y[/tex].

We have:

[tex]y=118(300)[/tex]

∴ [tex]y=35400[/tex]

Thus, Sarah will walk 35,400 steps in 5 hours.

Therefore, Andrew walks more steps than Sarah as [tex]36,000>35,400[/tex].