Question 169766
If the speed of the faster train is {{{r}}} then the speed of the slower train must be {{{r-20}}}.  Since the trains are going in opposite directions, the speed that they are moving relative to each other is the sum of their speeds, or {{{r + r -20}}}.


Since distance equals rate times time, or {{{d=rt}}} and the distance is given as 770 miles and the time as 7 hours, we can say:


{{{770=(r+r-20)7}}}


{{{770=(2r-20)7}}}


{{{770=14r-140}}}


{{{14r=910}}}


{{{r = 910/14 = 65}}}


So the westbound (faster) train was going 65 mph, and the eastbound (slower) train was going 20 mph less than that or 45 mph.


Check:  The sum of the speeds is 65 + 45 = 110.  7 hours at 110 mph is 770 miles.  Answer checks.