Final answer:
The actual distance traveled is calculated by dividing the odometer reading by the circumference ratio of the new tires to the original. For an odometer reading of 75,000 miles and tire circumferences of 106.19 inches and 80.33 inches respectively, the actual distance traveled is approximately 56,770 miles, with the closest answer from the options being 65,000 miles.
Step-by-step explanation:
The student's question involves calculating the actual distance traveled by a car, given a change in tire circumference from the factory default. The odometer reading is 75,000 miles with tires of a 106.19 inches circumference, but the original tires had a circumference of 80.33 inches.
To find the actual miles traveled, we must compare the differences in the revolutions made by the two sets of tires due to their different circumferences. We do this by creating a ratio of the circumferences:
(106.19 inches) / (80.33 inches) = 1.321.
This ratio tells us that for every mile the new tires say we've traveled, we've actually only traveled 1/1.321 miles, because the new tires make fewer revolutions per mile than the original tires.
To calculate the actual distance traveled we divide the odometer reading by the ratio:
75,000 miles / 1.321 = 56,770 miles (approximately).
Therefore, the closest answer to the actual miles traveled would be (a) 65,000 miles, since it is the nearest higher option provided.