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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 a is the time in hours to represent the motion of the faster car. (1 point)
The equation for the faster car can be written as:
y = 45a
To write an equation representing the motion of the faster car, we can use the formula for speed, which is distance divided by time.
For the first road, the car can go 60 miles in 2 hours, so the speed would be:
60 miles / 2 hours = 30 miles per hour
For the second road, the car can go 90 miles in 4 hours, so the speed would be:
90 miles / 4 hours = 22.5 miles per hour
Since we want to represent the motion of the faster car, we will use the speed of the first road, which is 30 miles per hour.
Therefore, the equation representing the motion of the faster car is:
y = 30a
Where y is the distance in miles and a is the time in hours.
To write an equation representing the motion of the faster car, we can use the formula for speed, which is given by speed = distance/time.
Let's first find the speed of the car on Road 1. We are given that the car can go 60 miles in 2 hours. So, the speed of the car on Road 1 is 60 miles/2 hours, which simplifies to 30 miles per hour.
Next, let's find the speed of the car on Road 2. We are given that the car can go 90 miles in 4 hours. So, the speed of the car on Road 2 is 90 miles/4 hours, which simplifies to 22.5 miles per hour.
Since we want an equation where y represents the distance in miles and a represents the time in hours, we can write the equation as:
y = 30a
This equation represents the motion of the faster car, where y is the distance in miles and a is the time in hours.
Wrong
Apologies for the incorrect response earlier.
To determine the equation representing the motion of the faster car, we need to compare the rates of the two different roads.
For Road 1, the car can go 60 miles in 2 hours. Thus, the speed on Road 1 is equal to 60 miles/2 hours, or 30 miles per hour.
For Road 2, the car can go 90 miles in 4 hours. Therefore, the speed on Road 2 is equal to 90 miles/4 hours, or 22.5 miles per hour.
Since we are looking for the equation representing the motion of the faster car, we need to use the higher speed, which is 30 miles per hour on Road 1.
Hence, the correct equation is:
y = 30a
where y represents the distance in miles and a represents the time in hours.