hey bot 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)
Apologies for the incorrect response earlier. Let's reassess the problem.
To represent the motion of the faster car, we need to determine the rate at which it travels. We can do this by calculating the average speed using the given information.
On Road 1, the car can go 60 miles in 2 hours. Therefore, the average speed on Road 1 is 60 miles / 2 hours = 30 miles per hour.
On Road 2, the car can go 90 miles in 4 hours. Therefore, the average speed on Road 2 is 90 miles / 4 hours = 22.5 miles per hour.
Since the faster car would have a higher average speed, we will use the speed of 30 miles per hour from Road 1 to represent its motion.
Thus, the equation representing the motion of the faster car is:
y = 30x
where y is the distance in miles and x is the time in hours.
nope
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correct
Thank you for confirming the correctness of the equation. If you have any more questions or need further assistance, feel free to ask.
The equation that represents the motion of the faster car can be written as:
y = mx
Given that the car on Road 1 can go 60 miles in 2 hours, we can find the rate of motion (m) as follows:
m = y / x = 60 miles / 2 hours = 30 miles/hour
Therefore, the equation representing the motion of the faster car would be:
y = 30x
To write an equation representing the motion of the faster car, we can calculate the rate (speed) at which the car travels on each road.
For Road 1, the car travels 60 miles in 2 hours, so the rate of the car on Road 1 is 60 miles / 2 hours = 30 miles per hour.
For Road 2, the car travels 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 want to represent the motion of the faster car, we will use the faster rate, which is 30 miles per hour.
Therefore, the equation representing the motion of the faster car is:
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, we need to analyze the given information about both roads.
For Road 1:
Distance (y1) = 60 miles
Time (x1) = 2 hours
For Road 2:
Distance (y2) = 90 miles
Time (x2) = 4 hours
We know that the faster car traveled on Road 2, so we will use the information from Road 2 to create the equation.
The equation representing the motion of the faster car can be written as:
y = mx + b
To find the equation, we need to determine the values of m (slope) and b (y-intercept).
The slope (m) represents the rate at which the car is traveling. In this case, it is the distance covered per hour. We can calculate it by dividing the change in distance by the change in time:
m = (y2 - y1) / (x2 - x1)
= (90 miles - 60 miles) / (4 hours - 2 hours)
= 30 miles / 2 hours
= 15 miles per hour
The y-intercept (b) represents the starting point of the motion. Since we don't have any information about it, we assume it to be zero.
Therefore, the equation becomes:
y = 15x + 0
y = 15x
This equation represents the motion of the faster car, where y is the distance in miles and x is the time in hours.