Answer
$200 \text{ } mph$
Work Step by Step
Let $x$ be the speed of the car. Using $D=rt,$ then, for the car,
\begin{array}{l}\require{cancel}
150=xt
\\\\
\dfrac{150}{x}=t
\\\\
t_{car}=\dfrac{150}{x}
.\end{array}
Using $D=rt,$ then, for the plane,
\begin{array}{l}\require{cancel}
600=(x+150)t
\\\\
\dfrac{600}{x+150}=t
\\\\
t_{plane}=\dfrac{600}{x+150}
.\end{array}
Since both time are given to be the same, then
\begin{array}{l}\require{cancel}
t_{car}=t_{plane}
\\\\
\dfrac{150}{x}=\dfrac{600}{x+150}
.\end{array}
By cross-multiplication and by the properties of equality, then
\begin{array}{l}\require{cancel}
150(x+150)=x(600)
\\\\
150x+22500=600x
\\\\
22500=600x-150x
\\\\
22500=450x
\\\\
\dfrac{22500}{450}=x
\\\\
50=x
.\end{array}
Hence, the speed of the plane, $x+150,$ is $
200 \text{ } mph
.$
