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 can go 60 miles in 2 hours, so the rate of motion is 60 miles / 2 hours = 30 miles/hour.
For Road 2, the car can go 90 miles in 4 hours, so the rate of motion is 90 miles / 4 hours = 22.5 miles/hour.
Since we want to represent the motion of the faster car, we will use the rate of motion of Road 1, which is 30 miles/hour.
Therefore, the equation is:
y = 30x
To write the equation representing the motion of the faster car, we can use the equation of a line in slope-intercept form: y = mx + b.
We know that on Road 1, the car can go 60 miles in 2 hours. This gives us a rate of 60/2 = 30 miles per hour.
Similarly, on Road 2, the car can go 90 miles in 4 hours, which gives us a rate of 90/4 = 22.5 miles per hour.
Since the car on Road 2 is faster, we will use its rate as the slope, m, in our equation.
Therefore, the equation representing the motion of the faster car is y = 22.5x.
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. We can find this rate by dividing the distance traveled by the time taken.
On Road 1, the car can go 60 miles in 2 hours. So, the rate of the car on Road 1 is 60 miles / 2 hours = 30 miles per hour.
On Road 2, the car can go 90 miles in 4 hours. So, the rate of the car on Road 2 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 faster rate, which is 30 miles per hour. The equation can be written as:
y = 30x
where y represents the distance in miles and x represents the time in hours for the faster car.