Two cars travel at constant rates. The rate at which car [tex]$M$[/tex] travels can be modeled by the equation [tex]y = 50x[/tex], where [tex]y[/tex] is the number of miles traveled given the number of hours spent traveling, [tex]x[/tex].
The table represents the travel for car [tex]$P$[/tex]. [tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Time Traveled (hours)} & \text{Distance Traveled (miles)} \\
\hline 2 & 90 \\
\hline 4 & 180 \\
\hline
\end{tabular}
\][/tex]
Compare the rates at which the two cars travel. Select from the drop-down lists to complete the sentences correctly.
Car [tex]$M$[/tex] travels at a [tex]$\square$[/tex] rate than car [tex]$P$[/tex]. Every hour, car [tex]$M$[/tex] will travel [tex]$\square$[/tex] miles [tex]$\square$[/tex] than car [tex]$P$[/tex].
Let's break down the problem step-by-step to compare the travel rates of car M and car P.
### Step 1: Understanding the Travel Rate of Car M The travel rate of car M is given by the equation [tex]\( y = 50x \)[/tex], where [tex]\( y \)[/tex] is the number of miles traveled and [tex]\( x \)[/tex] is the time in hours. This means that car M travels at a constant rate of 50 miles per hour.
### Step 2: Extract Data for Car P The table provides the travel data for car P: - After 2 hours, car P has traveled 90 miles. - After 4 hours, car P has traveled 180 miles.
### Step 3: Calculate the Travel Rate of Car P To find the travel rate of car P, we use the information from the table. We know the distance traveled and the time it took to travel that distance.
Using the data for 4 hours: [tex]\[ \text{Rate of car P} = \frac{\text{Distance}}{\text{Time}} = \frac{180 \text{ miles}}{4 \text{ hours}} = 45 \text{ miles per hour} \][/tex]
### Step 4: 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.
Now, we compare the two rates: - 50 miles per hour (car M) is greater than 45 miles per hour (car P). - The difference in the rates is [tex]\( 50 - 45 = 5 \)[/tex] miles per hour.
### Conclusions - Car M travels at a greater rate than car P. - Every hour, car M will travel 5 miles faster than car P.
Thus, the final sentences are: Car M travels at a greater rate than car P. Every hour, car M will travel 5 miles faster than car P.
