Final answer:
Rafael's distance to his destination is a linear function of his driving time. By solving a system of equations, we find the equation that represents this relationship. Using the equation, we can determine the distance after 72 minutes of driving.
Step-by-step explanation:
In this scenario, Rafael's distance to his destination is a linear function of his driving time. We can create an equation with this linear relationship using the given information. Let's start with the equation:
d = mt + b
where d represents the distance, t represents the time, m represents the slope, and b represents the y-intercept.
Using the first set of data (52 miles after 40 minutes), we can substitute the values into the equation:
52 = 40m + b
Next, using the second set of data (39.4 miles after 58 minutes), we can substitute the values again:
39.4 = 58m + b
We now have a system of equations. We can solve this system to find the values of m and b.
Using either substitution or elimination methods, we find that m = -0.35 and b = 66.6.
Now we can use the equation d = -0.35t + 66.6 to find the distance after 72 minutes of driving:
d = -0.35(72) + 66.6
Simplifying the equation, we get:
d = 36.4
Therefore, Rafael will have approximately 36.4 miles to his destination after 72 minutes of driving. So, the correct option is Option 3: 36.4 miles.