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.
The equation for the motion of the faster car can be written as:
y = mx + b
where y represents the distance in miles and x represents the time in hours. To find the equation, we need to determine the values of m and b.
On Road 1, the car can go 60 miles in 2 hours. This gives us one set of coordinates: (2, 60).
On Road 2, the car can go 90 miles in 4 hours. This gives us another set of coordinates: (4, 90).
We can now use these coordinates to find the slope, m, and the y-intercept, b.
The slope, m, can be calculated using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the values from Road 1, we have:
m = (60 - 0) / (2 - 0) = 60 / 2 = 30
Substituting the values from Road 2, we have:
m = (90 - 0) / (4 - 0) = 90 / 4 = 22.5
We can see that the car on Road 1 is faster since it covers 30 miles in 1 hour, while the car on Road 2 covers 22.5 miles in 1 hour.
Now, let's find the y-intercept, b.
Using the coordinates of Road 1, we can substitute the values (2, 60):
y = mx + b
60 = 30(2) + b
60 = 60 + b
b = 60 - 60
b = 0
Using the coordinates of Road 2, we can substitute the values (4, 90):
y = mx + b
90 = 22.5(4) + b
90 = 90 + b
b = 90 - 90
b = 0
Since both equations have a y-intercept of 0, the equation representing the motion of the faster car is:
y = 30x
which of these objects is moving at a rate of 2 feet per second
To determine which object is moving at a rate of 2 feet per second, we need more information about the objects in question. Without any additional context, it is not possible to determine which object is moving at a rate of 2 feet per second.
Let's assume that the faster car is driving on Road 2, where it can go 90 miles in 4 hours.
To write the equation, we need to express the relationship between the distance traveled (y) and the time taken (x).
We can use the formula for speed, which is distance divided by time:
Speed = Distance / Time
We can rearrange this equation to solve for distance:
Distance = Speed * Time
In this case, the speed is constant throughout the journey on Road 2, as it is the faster car. So, we can rewrite the equation as:
y = (Speed of the car on Road 2) * x
Since the car on Road 2 can go 90 miles in 4 hours, we can substitute the values:
y = (90 miles / 4 hours) * x
Simplifying this equation, we have:
y = 22.5x
Therefore, the equation to represent the motion of the faster car is: y = 22.5x, 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, we need to determine the rate at which the car is traveling on each road.
For Road 1, the car can go 60 miles in 2 hours. This means it is traveling at a rate of 60 miles / 2 hours = 30 miles per hour. So, the equation for Road 1 can be written as:
Distance (y) = Rate (30 miles/hour) * Time (x)
For Road 2, the car can go 90 miles in 4 hours. This means it is traveling at a rate of 90 miles / 4 hours = 22.5 miles per hour. So, the equation for Road 2 can be written as:
Distance (y) = Rate (22.5 miles/hour) * Time (x)
Since we are looking for the equation representing the motion of the faster car, we will use the equation for Road 1, as it has a faster rate. Therefore, the equation for the motion of the faster car is:
Distance (y) = 30 miles/hour * Time (x)