To find an equation that represents the motion of the faster car, we first need to determine the speed (rate) of each car based on the information given.
For Road 1:
- The car can go 60 miles in 2 hours.
- To find the speed (slope), we divide the distance by time:
\[ \text{Speed for Road 1} = \frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ miles per hour} \]
For Road 2:
- The car can go 90 miles in 4 hours.
- Similarly, we calculate the speed:
\[ \text{Speed for Road 2} = \frac{90 \text{ miles}}{4 \text{ hours}} = 22.5 \text{ miles per hour} \]
The faster car is the one on Road 1, which has a speed of 30 miles per hour.
Now we can write the equation for distance using the formula:
\[
y = mx
\]
where \(m\) is the speed (slope of the line), \(y\) is the distance in miles, and \(x\) is the time in hours.
Since the faster car travels at 30 miles per hour, the equation will be:
\[
y = 30x
\]
So, the equation that represents the motion of the faster car is:
\[
y = 30x
\]
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