Question

select the correct answer from each drop-down menu.

mike and breanna like to run after swim practice each day. usually they run the same distance, \\(x\\) miles. today, however, they ran different distances.

• mike ran at 7 miles per hour and ran 2 more miles than usual.
• breanna ran at 6 miles per hour and ran 1 more mile than usual.

complete the table to show each persons distance and rate, which could be used to create rational equation relating their distance, rate, and time.

\

$$\begin{tabular}{|l|l|l|} \\hline & distance & rate \\\\ \\hline mike & choose an answer & choose an answer \\\\ \\hline breanna & choose an answer & choose an answer \\\\ \\hline \\end{tabular}$$

Explanation:

Identify the given information

We are given the following details about Mike and Breanna's run today:

• Their usual distance is \(x\) miles.
• Mike ran at a rate of \(7\) miles per hour and ran \(2\) more miles than usual.
• Breanna ran at a rate of \(6\) miles per hour and ran \(1\) more mile than usual.

Determine Mike's distance and rate

Using the Mathematical Modeling concept, we translate the verbal descriptions into algebraic expressions:

• Mike's distance: Since he ran \(2\) miles more than his usual distance \(x\), his distance is \(x + 2\).
• Mike's rate: His speed is given directly as \(7\) miles per hour.

Determine Breanna's distance and rate

Using the Mathematical Modeling concept, we translate Breanna's details:

• Breanna's distance: Since she ran \(1\) mile more than her usual distance \(x\), her distance is \(x + 1\).
• Breanna's rate: Her speed is given directly as \(6\) miles per hour.

Complete the table values

We match the derived expressions and values to the corresponding drop-down menus in the table:

• Mike's Distance: \(x + 2\)
• Mike's Rate: \(7\)
• Breanna's Distance: \(x + 1\)
• Breanna's Rate: \(6\)

Answer:

• Mike's Distance: \(x + 2\)
• Mike's Rate: \(7\)
• Breanna's Distance: \(x + 1\)
• Breanna's Rate: \(6\)