Let's analyze the information given and compare the rates at which cars M and P travel.
### Step 1: Determine the rate of car M
The rate at which car M travels can be modeled by the equation [tex]\( y = 50x \)[/tex], where [tex]\( y \)[/tex] is the distance traveled and [tex]\( x \)[/tex] is the time in hours. Here, the coefficient of [tex]\( x \)[/tex] in the equation 50 indicates that car M travels 50 miles per hour.
### Step 2: Determine the rate of car P
To find the rate (speed) at which car P travels, we need to use the data provided in the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time Traveled (hours)} & \text{Distance Traveled (miles)} \\
\hline
2 & 90 \\
\hline
4 & 180 \\
\hline
\end{array}
\][/tex]
We can calculate the rate of car P for each row in the table and then average these rates.
From the table:
- At 2 hours, car P travels 90 miles. Thus, the rate is:
[tex]\[ \text{Rate}_1 = \frac{90\text{ miles}}{2\text{ hours}} = 45 \text{ miles per hour} \][/tex]
- At 4 hours, car P travels 180 miles. Thus, the rate is:
[tex]\[ \text{Rate}_2 = \frac{180\text{ miles}}{4\text{ hours}} = 45 \text{ miles per hour} \][/tex]
Since both rates are the same, the average rate at which car P travels is:
[tex]\[ \text{Rate}_P = \frac{45 + 45}{2} = 45 \text{ miles per hour} \][/tex]
### Step 3: Compare the rates
Now, we can compare the rates of car M and car P.
- Car M travels at 50 miles per hour.
- Car P travels at 45 miles per hour.
Clearly, car M travels faster than car P. The difference in their rates is:
[tex]\[ 50 \text{ miles per hour} - 45 \text{ miles per hour} = 5 \text{ miles per hour} \][/tex]
### Conclusion
Using the information we calculated, we can complete the sentences as follows:
Car [tex]\( M \)[/tex] travels at a faster rate than car [tex]\( P \)[/tex]. Every hour, car [tex]\( M \)[/tex] will travel 5 miles more than car [tex]\( P \)[/tex].
