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 if the faster car.
Let's assume the faster car can travel at a constant speed of "s" miles per hour. We can then write the equation for the first road as:
60 = 2s
Similarly, the equation for the second road is:
90 = 4s
We can simplify both equations by dividing both sides by the respective time:
30 = s and 22.5 = s
So, the equation representing the motion of the faster car is:
y = 30x
To write an equation that represents the motion of the faster car, we can use the information given for Road 2, where the car can go 90 miles in 4 hours.
Let's assign y as the distance in miles and x as the time in hours.
From the given information, we know that the car goes 90 miles in 4 hours. This can be expressed as:
y = 90x / 4
Simplifying this equation, we get:
y = 22.5x
Therefore, the equation that represents the motion of the faster car is:
y = 22.5x
To write the equation representing the motion of the faster car, we need to determine its rate or speed. We can find the rate by dividing the distance by the time taken.
For Road 1, the car can go 60 miles in 2 hours. So, the rate or speed on Road 1 is 60 miles / 2 hours = 30 miles per hour.
Similarly, for Road 2, the car can go 90 miles in 4 hours. So, the rate or speed on Road 2 is 90 miles / 4 hours = 22.5 miles per hour.
Since the faster car is the one with the higher speed, we will use the rate of 30 miles per hour (from Road 1) for the equation.
The equation representing the motion of the faster car is:
y = 30x
Here, y represents the distance in miles (since it is on the y-axis), and x represents the time in hours (since it is on the x-axis). So, y = 30x means that the distance (y) is equal to the speed (30 miles per hour) multiplied by the time (x).