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)
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For Road 1, the car travels at a rate of 60 miles in 2 hours. We can write this as the equation:
$$\frac{60}{2} = \frac{y}{x}$$
For Road 2, the car travels at a rate of 90 miles in 4 hours. We can write this as the equation:
$$\frac{90}{4} = \frac{y}{x}$$
Since we want to represent the motion of the faster car, we will use the equation for Road 2, which yields:
$$\frac{90}{4} = \frac{y}{x}$$
To write an equation representing the motion of the faster car, we need to determine its speed first.
For Road 1, the car goes 60 miles in 2 hours, so its speed is 60 miles / 2 hours = 30 miles per hour.
For Road 2, the car goes 90 miles in 4 hours, so its speed is 90 miles / 4 hours = 22.5 miles per hour.
Since we are looking for the equation representing the motion of the faster car, we will use the speed of Road 1, which is 30 miles per hour.
The equation representing the motion of the faster car would be:
y = 30x
where y is the distance in miles and x is the time in hours.
To write an equation representing the motion of the faster car, let's first analyze the given information.
On Road 1, the car can go 60 miles in 2 hours. This means the car is traveling at a constant speed of 60 miles / 2 hours = 30 miles per hour.
On Road 2, the car can go 90 miles in 4 hours. This means the car is traveling at a constant speed of 90 miles / 4 hours = 22.5 miles per hour.
Since we want to represent the motion of the faster car, we will use the faster speed of 30 miles per hour.
The equation representing the motion of the faster car can be written as:
y = 30x
where y is the distance in miles and x is the time in hours. This equation states that as time (x) increases, the distance traveled (y) increases at a rate of 30 miles per hour.