Make this chart.

         D      R      T
Ruth    
Nadia   


We want to know Nadia's speed, so we put x for
Nadia's rate (speed):


         D      R      T
Ruth    
Nadia           x       

>>...Ruth...headed south...at an average of 25 mph.

So we put 25 for Ruth's speed

         D      R      T
Ruth           25     
Nadia           x       

Ruth traveled from 4 AM to 5 PM, which is 13
hours. So we put 13 for Ruth's time


         D      R      T
Ruth           25     13
Nadia           x       


Now we use D=RT to get Ruth's total distance at 5PM. 

D = (25)(13) = 325 miles, so we put 325 for Ruth's
distance


         D      R      T
Ruth    325    25     11
Nadia           x       

Nadia traveled from 11 AM to 5 PM, so her time was 6 hours.
So we put 6 for Nadia's time.


         D      R      T
Ruth    325    25     11
Nadia           x      6 

Now we use D=RT to get Nadia's total distance at 5PM. 

D = (x)(6) = 6x miles, so we put 6x for Nadia's
distance


         D      R      T
Ruth    325    25     11
Nadia    6x     x      6 

Now that the chart is complete, we make the equation from
what we didn't use to make the chart.  That was this:

>>...By 5:00 p.m. the same day Nadia was 17 miles ahead of Ruth...<<

So Nadia's distance = Ruth's distance + 17, so

                 6x = 325 + 17 
                 6x = 342

Divide both sides by 6 

                  x = 57 mph

Edwin