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 fastest car.
To represent the motion of the fastest car, we need to determine the speed (rate) at which the car is traveling on each road.
On Road 1, the car can go 60 miles in 2 hours, so its speed is calculated by dividing the distance by the time:
Speed on Road 1 = 60 miles / 2 hours = 30 miles per hour.
On Road 2, the car can go 90 miles in 4 hours, which can be expressed as:
Speed on Road 2 = 90 miles / 4 hours = 22.5 miles per hour.
Since we are looking for the fastest car, we want to consider the car that is traveling at the higher speed. In this case, the car traveling at 30 miles per hour on Road 1 is faster than the car traveling at 22.5 miles per hour on Road 2.
Therefore, the equation representing the motion of the fastest car is:
y = 30x, where y is the distance in miles and x is the time in hours.