Answer
The first train travels in $45$ $mph$ and the second train in $60$ $mph.$
Work Step by Step
Let $x$ be the speed of the first train. Then $x+15$ is the speed of the second train.
Using $D=rt,$ then the conditions of the problem for the first train is
\begin{array}{l}\require{cancel}
D_1=x(6)
\\\\
D_1=6x
.\end{array}
Using $D=rt,$ then the conditions of the problem for the first train is
\begin{array}{l}\require{cancel}
D_2=(x+15)(6)
\\\\
D_2=6x+90
.\end{array}
Since the distances covered by the two trains sum to $630$ miles, then
\begin{array}{l}\require{cancel}
630=D_1+D_2
.\end{array}
Substituting the equivalences of $D_1$ and $D_2$ respectively and using the properties of equality, then
\begin{array}{l}\require{cancel}
630=6x+6x+90
\\\\
630-90=6x+6x
\\\\
540=12x
\\\\
\dfrac{540}{12}=x
\\\\
x=45
.\end{array}
Hence, the first train travels in $x$ or $45$ $mph$ and the second train in $x+15$ or $60$ $mph.$
