Answer
The family must drive at least $7.\overline{27}$ hours per day.
Work Step by Step
Let h be the number of hours driven. Given an average speed of 55 miles per hour, the number of miles driven is 55h. If the goal is to drive at least 400 miles per day, the number of miles driven must be greater than or equal to 400.
$55h\geq400\longrightarrow$ divide both sides by 55
$55h\div55\geq400\div55\longrightarrow$ divide
$h\geq7.\overline{27}$
