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Let's recall the formula that describes the relation between distance, speed and time. $\begin{gathered} d=st \end{gathered}$ Since we are asked for the speed, let's isolate $s.$ $s=\frac{d}{t}$ The family Humphrey needs to get there before the hotel is closed to be able to check in. Thus, the speed has to be greater than the distance divided by time. $s\gt\frac{d}{t}$ We should now substitute the distance with $250$ and the time with $5.$
$s\gt\dfrac{d}{t}$
$s>\dfrac{250}{5}$
$s \gt 50$
The solution $s \gt 50$ means the family should travel at a speed greater than $50$ mph.