Answer
$54 \text{ }mph$
Work Step by Step
The back-and-forth distance from the lake house to home is
\begin{array}{l}\require{cancel}
2(121.5)
\\=
243
.\end{array}
Using $D=rt,$ then
\begin{array}{l}\require{cancel}
243=r(4.5)
\\
\dfrac{243}{4.5}=r
\\
r=54
.\end{array}
Hence the average speed, $r,$ is $
54 \text{ }mph
.$
