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.
To write the equation representing the motion of the faster car, we need to determine which car is faster. We can compare the rates at which both cars travel.
For Road 1, the car can go 60 miles in 2 hours. Thus, the rate of the car on Road 1 is given by 60 miles/2 hours = 30 miles/hour.
For Road 2, the car can go 90 miles in 4 hours. Thus, the rate of the car on Road 2 is given by 90 miles/4 hours = 22.5 miles/hour.
Comparing the rates, we can see that the car on Road 1 is faster than the car on Road 2.
Hence, we will write the equation representing the motion of the car on Road 1.
Let y be the distance in miles and x be the time in hours for the car on Road 1.
The equation representing the motion of the car on Road 1 would be:
y = 30x
To write an equation representing the motion of the faster car, we need to determine the rate at which the car is traveling.
Let's calculate the rate of the car on Road 1. The car travels 60 miles in 2 hours, which means the rate is given by:
Rate (Road 1) = Distance / Time = 60 miles / 2 hours = 30 miles/hour
Now, let's calculate the rate of the car on Road 2. The car travels 90 miles in 4 hours, so the rate is:
Rate (Road 2) = Distance / Time = 90 miles / 4 hours = 22.5 miles/hour
Since the question asks for the equation representing the motion of the faster car, we'll use the rate of the faster car, which is 30 miles/hour (from Road 1).
Therefore, the equation representing the motion of the faster car is:
Distance (y) = Rate (Road 1) * Time (x) = 30 miles/hour * x hours
Thus, the equation is:
y = 30x
To write an equation representing the motion of the faster car, we need to use the information given about Road 2, where the car can go 90 miles in 4 hours.
Let's use the equation y = mx + b, where y represents the distance (in miles), x represents the time (in hours), m represents the speed (in miles per hour), and b represents the y-intercept (the starting point).
From the information given about Road 2, we know that the car can go 90 miles in 4 hours. This means that the speed of the car (m) is 90 divided by 4, which is 22.5 miles per hour.
Therefore, the equation representing the motion of the faster car is y = 22.5x.