Let d be the number of additional days the family needs to travel to reach a distance of 1,600 miles.
The total distance traveled can be expressed as:
200 + 350d
We want this distance to equal 1,600 miles, so we can set up the equation:
200 + 350d = 1,600
Subtracting 200 from both sides, we get:
350d = 1,400
Dividing both sides by 350, we get:
d = 4
Therefore, the family will need to travel for an additional 4 days to reach a distance of 1,600 miles.