To compare the rates at which car M and car P travel, we'll first determine the travel rates for each car.
### Step 1: Determine the Rate for Car M
The rate at which car M travels is given by the equation:
[tex]\[ y = 50x \][/tex]
In this equation, [tex]\( y \)[/tex] is the number of miles traveled, and [tex]\( x \)[/tex] is the number of hours spent traveling. This indicates that car M travels at a rate of 50 miles per hour.
### Step 2: Determine the Rate for Car P
We have a table that represents the travel for car P with corresponding times and distances:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time Traveled (hours)} & \text{Distance Traveled (miles)} \\
\hline
2 & 90 \\
\hline
4 & 180 \\
\hline
\end{array}
\][/tex]
From the table:
- In 2 hours, car P travels 90 miles.
- In 4 hours, car P travels 180 miles.
Now, calculate the rate (speed) of car P:
[tex]\[ \text{Rate of car P} = \frac{\text{Distance}}{\text{Time}} = \frac{90 \text{ miles}}{2 \text{ hours}} = 45 \text{ miles per hour} \][/tex]
We can confirm this rate using the second data point:
[tex]\[ \text{Rate of car P} = \frac{180 \text{ miles}}{4 \text{ hours}} = 45 \text{ miles per hour} \][/tex]
### Step 3: Compare the Rates of Car M and Car P
- Car M's rate: 50 miles per hour.
- Car P's rate: 45 miles per hour.
### Step 4: Conclusion
Comparing these rates:
- Car M travels at a faster rate than car P because 50 miles per hour is greater than 45 miles per hour.
- The difference in their rates is [tex]\(50 - 45 = 5\)[/tex] miles per hour.
This means every hour, car M will travel 5 more miles than car P.
Therefore, the completed sentences are:
Car M travels at a faster rate than car P. Every hour, car M will travel 5 miles more than car P.
