To compare the rates at which the two cars travel, let's break down the given information and complete the task step by step.
### Calculating the Rate of Car P
From the table:
- In 2 hours, car P travels 90 miles.
- In 4 hours, car P travels 180 miles.
Let's determine the rate of car P.
The rate (or speed) is given by the formula:
[tex]\[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} \][/tex]
Using the second row from the table for accuracy:
[tex]\[ \text{Rate of Car P} = \frac{180 \text{ miles}}{4 \text{ hours}} = 45 \text{ miles per hour} \][/tex]
### Given Rate of Car M
The rate at which car M travels is provided in the equation [tex]\( y = 50x \)[/tex], meaning car M travels at [tex]\(\mathbf{50}\)[/tex] miles per hour.
### Comparing the Rates
- Car M travels at 50 miles per hour.
- Car P travels at 45 miles per hour.
We can now compare the rates:
- Car M travels at a faster rate than car P.
### Calculating the Difference
The difference in their rates is:
[tex]\[ 50 \text{ miles per hour} - 45 \text{ miles per hour} = 5 \text{ miles per hour} \][/tex]
So, every hour, car M travels 5 miles more than car P.
### Completing the Sentences
1. Car [tex]\(M\)[/tex] travels at a faster rate than car P.
2. Every hour, car M will travel 5 miles more than car P.
Thus, the completed sentences are as follows:
- Car [tex]\(M\)[/tex] travels at a faster rate than car P.
- Every hour, car M will travel 5 miles more than car P.
