Final answer:
The Smith family traveled 631.7 miles on their vacation.
Step-by-step explanation:
To find out how far the Smith family traveled on their vacation, we need to calculate the difference between the odometer readings when they left and when they arrived. The initial odometer reading is 38,573.2 miles and the final reading is 39,204.9 miles. To calculate the difference in distance, we subtract the initial reading from the final reading: 39,204.9 - 38,573.2 = 631.7 miles. Therefore, the Smith family traveled 631.7 miles on their vacation.