Final answer:
The Gibbons family traveled 500 miles on the first day and 425 miles on the second day to reach their vacation home.
Step-by-step explanation:
To solve the problem we will let the number of miles traveled on the second day be x. Since they traveled 75 miles more on the first day, the first day's travel distance will be x + 75 miles. They traveled a total of 925 miles over the two days, so we can write the equation:
x + (x + 75) = 925
Solving for x gives us:
2x + 75 = 925
2x = 925 - 75
2x = 850
x = 850 / 2
x = 425
Therefore, the Gibbons family traveled 425 miles on the second day and 425 + 75 = 500 miles on the first day.