Final answer:
Gas mileage varies with the driving speed of a car. To answer the question, we need to use linear equations to find the relationship between speed and gas mileage. Then, we can substitute the given values of x and y into the equation to find the gas mileage at x hours and y hours.
Step-by-step explanation:
The subject of this question is Mathematics and it is at a High School grade level.
To answer parts (a) and (b), we need to know the relationship between the speed of a car and its gas mileage. Let's say the car averages m miles per gallon on the highway when the average speed is s miles per hour. We are given two data points: m1 for s1 and m2 for s2. We can use a linear equation to find the relation between speed and gas mileage.
(a) The equation for the relation is m = ks + b, where k is the slope and b is the y-intercept. Using the two data points, we can form two equations:
m1 = k * s1 + b and m2 = k * s2 + b
Solving these equations, we can find the values of k and b. Once we have these values, we can substitute the value of x (hours) into the equation m = ks + b to find the gas mileage at x hours.
(b) Similarly, we can substitute the value of y (hours) into the equation to find the gas mileage at y hours.