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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 $5.$
The solution $s \gt 50$ means the family should travel at a speed greater than $50$ mph.