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.
We can start by finding the rate of the car on each road.
For Road 1, the car can go 60 miles in 2 hours. Therefore, the rate of the car on Road 1 is 60 miles / 2 hours = 30 miles per hour.
For Road 2, the car can go 90 miles in 4 hours. Therefore, 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'll use the rate of the car on Road 1 (30 mph).
The equation to represent the motion of the faster car is:
y = 30x
where y is the distance in miles and x is the time in hours.
Let's use the equation y = mx + b, where y represents the distance in miles and x represents the time in hours.
For road 1, the car travels 60 miles in 2 hours. Therefore, the rate of travel (m) on road 1 is:
m = distance / time
m = 60 miles / 2 hours
m = 30 miles/hour
So, for road 1, the equation is:
y = 30x + b
Similarly, for road 2, the car travels 90 miles in 4 hours. Therefore, the rate of travel (m) on road 2 is:
m = distance / time
m = 90 miles / 4 hours
m = 22.5 miles/hour
So, for road 2, the equation is:
y = 22.5x + b
Since we want the equation for the motion of the faster car, we should use the equation for road 1, as its rate of travel (30 miles/hour) is greater than the rate of travel on road 2 (22.5 miles/hour). Therefore, the equation representing the motion of the faster car is:
y = 30x + b
To write an equation representing the motion of the faster car, we can use the formula:
distance = speed × time
Let's find the speed of the faster car.
For road 1, the car can go 60 miles in 2 hours. So, the speed of the car on road 1 can be calculated by dividing the distance by the time:
speed on road 1 = 60 miles ÷ 2 hours = 30 miles/hour
For road 2, the car can go 90 miles in 4 hours. So, the speed of the car on road 2 can be calculated by dividing the distance by the time:
speed on road 2 = 90 miles ÷ 4 hours = 22.5 miles/hour
Since we're looking for the equation representing the motion of the faster car, we'll use the higher speed, which in this case is 30 miles/hour.
Now we can write the equation using the information we have:
y = 30x
In this equation, y represents the distance the car traveled in miles, and x represents the time in hours.