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)
To represent the motion of the faster car, we can use the equation of a straight line, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope of the line. The slope of a line is equal to the ratio of the change in y (distance) to the change in x (time).
For Road 1, the car can go 60 miles in 2 hours. So, the slope for Road 1 is:
m1 = (60 miles) / (2 hours) = 30 miles/hour
For Road 2, the car can go 90 miles in 4 hours. So, the slope for Road 2 is:
m2 = (90 miles) / (4 hours) = 22.5 miles/hour
Since the faster car will have a higher speed, we'll use the larger slope, which is 30 miles/hour.
Now, let's write the equation using the slope and the given information about Road 1:
y = 30x + b
To find the y-intercept (b), we can use the coordinates of a point on Road 1. We know that the car can go 60 miles in 2 hours on Road 1. So, we have the point (2, 60).
Substituting these values into the equation, we can solve for b:
60 = 30(2) + b
60 = 60 + b
b = 60 - 60
b = 0
Therefore, the equation representing the motion of the faster car is:
y = 30x + 0
y = 30x
For Road 1, the car can go 60 miles in 2 hours. The equation representing this motion is:
y = 30x
For Road 2, the car can go 90 miles in 4 hours. The equation representing this motion is:
y = 22.5x
Since we are looking for the equation representing the motion of the faster car, we can use the equation for Road 2:
y = 22.5x
To find the equation that represents the motion of the faster car, we need to analyze the given information about Road 1 and Road 2.
On Road 1, the car can go 60 miles in 2 hours. This means that the car's speed on Road 1 is given by the formula:
Speed = Distance / Time
Speed = 60 miles / 2 hours
Speed = 30 miles/hour
Similarly, on Road 2, the car can go 90 miles in 4 hours. Using the same formula:
Speed = Distance / Time
Speed = 90 miles / 4 hours
Speed = 22.5 miles/hour
Since we want to represent the motion of the faster car, we can see that the car's speed on Road 1 (30 miles/hour) is greater than its speed on Road 2 (22.5 miles/hour).
Therefore, the equation that represents the motion of the faster car can be written as:
y = 30x
In this equation, y represents the distance traveled in miles, and x represents the time traveled in hours.