Final answer:
After determining the rate at which the distance to Tony's destination decreases per minute, we calculate that he will have approximately 26 miles remaining after 65 minutes of driving. Considering the answer options, we round to the nearest and conclude Option A, 25 miles.
Step-by-step explanation:
The question asks us to determine how many miles Tony will have to his destination after 65 minutes of driving if the distance to his destination is a linear function of his driving time. We have two points that describe this linear function: (33 minutes, 50 miles) and (51 minutes, 36.5 miles).
Let's find the slope of the line (rate of change of distance with respect to time), which is given by:
slope = (change in distance) / (change in time)= (50 miles - 36.5 miles) / (33 minutes - 51 minutes)= 13.5 miles / (-18 minutes)= -0.75 miles/minute
Now, we have the rate at which the distance to the destination decreases. We can apply this to find the distance to the destination after 65 minutes. Since we know Tony has 50 miles to go after 33 minutes, we calculate the additional time he drives to reach 65 minutes, which is 65 minutes - 33 minutes = 32 minutes. The additional distance covered in this time is:
distance = rate * time= -0.75 miles/minute * 32 minutes= -24 miles
Subtracting this distance from the distance at 33 minutes:
50 miles - 24 miles = 26 miles
Therefore, Tony will have approximately 26 miles to his destination after 65 minutes of driving, which isn't one of the options provided. However, since the answer choices are all exactly 5 miles apart, it's possible this is a real-world scenario where the distances are rounded, and we might round our answer to the nearest option. In this case, 26 miles would be rounded down to 25 miles (Option A).