Question 126593
For this problem you'll need to remember that rate x time = distance or {{{r*t = d}}}
We know that both trains travelled a distance that separated them by 280 miles after 2 hours. Therefore:

--The distance travelled by the northbound train (x) plus the distance travelled by the southbound train (y) totals 280 miles or, algebraically:
{{{x + y = 280}}}

1. Using our formula {{{r*t = d}}} we can substitute:
a. Let r = the speed of the northbound train 
b. Let {{{r + 20}}} = the speed of the southbound train (20 mph faster)
c. Both trains have travelled for 2 hours:
d. Let x = {{{2*r}}}  
e. Let y = {{{2*(r + 20)}}} 

2. Substitute for x and y and solve for r:
{{{2r + 2(r+20) = 280}}}
{{{2r + 2r + 40 = 280}}}
{{{4r = 240}}}
{{{r = 60}}}
{{{r + 20 = 80}}}
-The northbound train travels at 60 mph
-The southbound train travels at 80 mph (20 mph faster)

3. Check:
{{{2r + 2(r + 20) = 280}}}
{{{2(60) + 2((60) + 20) = 280}}}
{{{120 + 2(80) = 280}}}
{{{120 + 160 = 280}}}
{{{280 = 280}}}