Question 126593
One train is going {{{r[1]}}} mph, and the other is going {{{r[1] + 20}}} mph.  Since they are travelling in opposite directions, their speed relative to each other is the sum of their speeds, namely:  {{{r[1] + (r[1]+20)}}}


Using <i>distance = rate times time</i> {{{d=rt}}} in the form {{{r=d/t}}} and plugging in the values we know, we can calculate {{{r[1]}}}, the speed of the slower train.


What we know:


{{{d = 280}}}
{{{t = 2}}}
{{{r = r[1] + (r[1]+20)}}}


{{{r[1] + (r[1]+20)=280/2}}}
{{{2r[1]+20=140}}}
{{{2r[1]=120}}}
{{{r[1]=60}}}


So the slower train is going 60 mph, and the faster train is going 60 + 20 = 80 mph.


Check the answer:

One train goes 60 mph for 2 hours so it travels 120 miles.  The other train goes 80 mph for the same 2 hours so it travels 160 miles.  120 plus 160 = 280.  Answer checks.