Miguel drove for 8 hours at a constant rate. He drove a total of 424 miles.

Question

Donna also drove at a constant rate. This table shows the number of miles she had driven in different numbers of hours.

How do the unit rates compare?

Select from the drop-down menus to correctly complete the statement.

Miguel has a
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unit rate of change than Donna because
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is greater than
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.

Number of hours Total miles driven
3 144
6 288
9 432

Answer 1

To compare Miguel's and Donna's unit rates, we first need to calculate Miguel's unit rate (miles per hour) and then determine Donna's unit rate based on the data provided in the table.

Miguel's Unit Rate:

• Total miles driven: 424 miles
• Time: 8 hours
• Unit rate = Total miles / Time = 424 miles / 8 hours = 53 miles per hour.

Donna's Unit Rate: Now, let's calculate Donna's unit rate using the data provided in the table.

1. When Donna drove for 3 hours, she drove 144 miles:

   • Unit rate = 144 miles / 3 hours = 48 miles per hour.

2. When Donna drove for 6 hours, she drove 288 miles:

   • Unit rate = 288 miles / 6 hours = 48 miles per hour.

3. When Donna drove for 9 hours, she drove 432 miles:

   • Unit rate = 432 miles / 9 hours = 48 miles per hour.

Based on these calculations, Donna's unit rate remains consistent at 48 miles per hour for all times calculated.

Comparison:

• Miguel's unit rate is 53 miles per hour.
• Donna's unit rate is 48 miles per hour.

In conclusion, we can complete the statement as follows:

Miguel has a greater unit rate of change than Donna because 53 miles per hour is greater than 48 miles per hour.