a) Let x represent the minimum speed limit
Let y represent the maximum speed limit
Recall, distance = speed x time
From the information given,
Tony drove for 2 hours at the minimum speed and 3.5 hours at the maximum speed. This means that the distance covered while driving at the minimum speed is 2 * x = 2x and the distance covered while driving at the maximum speed is 3.5 * y = 3.5y. If the total distance covered was 355 miles, then the equation that represents Tony's distance is
2x + 3.5y = 355
Also, Rae drove for 2 hours at the minimum speed and 3 hours at the maximum speed. This means that the distance covered while driving at the minimum speed is 2 * x = 2x and the distance covered while driving at the maximum speed is 3 * y = 3y. If the total distance covered was 320 miles, then the equation that represents Rae's distance is
2x + 3y = 320
b) We would solve the equations by applying the method of elimination. Since the coefficient of x is these same in both equations, we would eliminate x by subtracting the second equation from the first equation. We have
2x - 2x + 3.5y - 3y = 355 - 320
0.5y = 35
Dividing both sides of the equation by 0.5, we have
y = 35/0.5
y = 70
We would find x by substituting y = 70 into any of the previous equations. Substituting y = 70 into 2x + 3y = 320, we have
2x + 3 * 70 = 320
2x + 210 = 320
Subtracting 210 from both sides of the equation, we have
2x + 210 - 210 = 320 - 210
2x = 110
Dividing both sides of the equation by 2, we have
x = 110/2 = 55
Thus,
Minimum speed limit = 55 miles per hour
Maximum speed limit = 70 miles per hour