Question

Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y
𝑦
is the distance in miles and x
𝑥
is the time in hours to represent the motion of the faster car.(1 point) .

Answer 1

To express the motion of the faster car, we first need to determine its speed from the given information.

1. For Road 1, the car travels 60 miles in 2 hours. The speed can be calculated as follows:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ miles per hour}
\]

2. For Road 2, the car travels 90 miles in 4 hours. The speed is:

\[
\text{Speed} = \frac{90 \text{ miles}}{4 \text{ hours}} = 22.5 \text{ miles per hour}
\]

Since the car is faster on Road 1, we'll use the speed from Road 1 to create the equation.

The equation that represents the distance \( y \) in miles for the car driving on Road 1 over time \( x \) in hours can be written in the form:

\[
y = 30x
\]

So the equation is:

\[
y = 30x
\]

This equation means that for every hour \( x \) the car drives, it covers 30 miles.