Answer
$R=54 \text{ mph}$
Work Step by Step
The variation model described by the problem is $
R=\dfrac{k}{T}
,$ where $R$ is the speed and $T$ is the time.
(A time of $6$ seconds is equivalent to $\dfrac{6}{60}$ hour and a time of $5$ seconds is equivalent to $\dfrac{5}{60}$ hour.)
Substituting the given values in the variation model above results to
\begin{array}{l}\require{cancel}
45=\dfrac{k}{6/60}
\\\\
45=\dfrac{k}{1/10}
\\\\
45=10k
\\\\
\dfrac{45}{10}=k
\\\\
k=\dfrac{9}{2}
.\end{array}
Therefore, the variation equation is
\begin{array}{l}\require{cancel}
R=\dfrac{9/2}{T}
\\\\
R=\dfrac{9}{2T}
.\end{array}
Using the variation equation above, then
\begin{array}{l}\require{cancel}
R=\dfrac{9}{2(5/60)}
\\\\
R=\dfrac{9}{10/60}
\\\\
R=\dfrac{9}{1/6}
\\\\
R=54
.\end{array}
Hence, the speed of the car, $R,$ is $
R=54 \text{ mph}
.$
