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 is the distance in miles and  x is the time in hours to represent the motion of the faster car.(1 point) please help me

Answer 1

Simplify the answer please

Answer 2

Correct thanks

Answer 3

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:
\[
y = 30x
\]

Answer 4

The equation that represents the motion of the faster car (on Road 1) can be simplified directly as follows:

\[
y = 30x
\]

This equation is already in its simplest form.

- **\(y\)** represents the distance in miles.
- **\(x\)** represents the time in hours.
- The coefficient \(30\) indicates that the car travels 30 miles for every hour of driving.

So, the simplest form of the equation is:

\[
y = 30x
\]

This means that for every hour (\(x\)), the car travels 30 miles (\(y\)).

Answer 5

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy driving!