2 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
Since we want to find the equation for the fastest car, we know that it reached the highest speed. To determine this, we can compare the speed of the two cars by finding their respective rates (distance/time).
For the first car on road 1, the rate is 60 miles / 2 hours = 30 miles per hour.
For the second car on road 2, the rate is 90 miles / 4 hours = 22.5 miles per hour.
Since the first car has a higher rate, it is the fastest car, and we want to represent its motion with an equation. Let's call this equation y = mx + b.
We already know that the rate (m) is 30 miles per hour. However, we need to determine the y-intercept (b) in order to complete the equation.
To do this, we can choose any point on the line y = mx + b that represents the motion of the fastest car. We can use the information given for the first car driving on road 1 where it can go 60 miles in 2 hours. Let's use this point (2, 60).
Substituting these values into the equation, we have:
60 = 30(2) + b
Simplifying:
60 = 60 + b
Subtracting 60 from both sides:
0 = b
Therefore, the equation for the motion of the fastest car is:
y = 30x.