Question

You are doing a walkathon/runathon to raise money for your school. You can walk at a rate of 4 miles per hour and run at a rate of 6 miles per hour. You need to cover more than 8 miles in order to raise your part of the money. Which of the following linear inequalities can be used to determine how long you must walk (w) and run (r) in order to cover more than 8 miles? O 4w + 6r > 8 4w + 65 = 8 O 4w + 6r > 8 O 4w + 6r

Answer 1

We need to determine which of the given inequalities can be used to determine how long you must walk (w) and run (r) in order to cover more than 8 miles.

We know that you can walk at a rate of 4 mi/h, and run at a rate of 6mi/h.

Thus, if you walk for w hours, you will walk a distance d₁, in miles, given by:

`d_1=4w`

Also, if you run r hours, you will run a distance d₂, in miles, given by:

`d_2=6r`

Now, notice that the total distance is the sum of d₁ and d₂. And the total distance, in miles, must be greater than 8.

We represent 'greater than' using the symbol '>':

`\begin{gathered} d_1+d_2>8 \\ \\ 4w+6r>8 \end{gathered}`

Therefore, the correct option is:

`4w+6r>8`