Question 175275
We know that Speed equals distance over time

{{{Speed=Distance/Time}}}

In this problem we are dealing with two speeds, Shelly's and Jack's
And we know that Jack's speed is 15 miles faster:

Jack's (J) = Shelly's (S) + 15
{{{J=S+15}}}

Then we know they have covered 315 miles (distance) after 3 hours (time)using their combined speeds. 
Since they are traveling opposite directions we need to add their speeds:


{{{J+S=Distance/time}}}   

We replace the known values for distance and speed:

{{{J+S=315/3}}} 


Remember that J=S+15 so we replace J with the expression s+15

{{{(S+15) + S = 105}}}

{{{2s + 15=105}}}

{{{2s=105-15}}}

{{{2s=90}}}

{{{s=90/2}}}

{{{s=45}}}

And we know that Jacks is 15 more
{{{J=S+15}}}
{{{J=45+15}}}
{{{j=60}}}

Jack's speed= 60 Miles per hour

Rate= Speed
Jacks= 60 Miles per hour
Shelly's = 45 Miles per hour