let

v1 = the speed of the first train

v2 = the speed of the second train

d = 360 mi

t = the total time of the travel for each train

one train is 20 mph faster than the other:

v2 = v1 + 20

since speed = distance/time we have distance = speed*time:

v1t + v2t = 360

plug v2 = v1 + 20 into last equation and solve for v2

v1t + (v1 + 20)t = 360

v1 + v1 + 20 = 360/t

v1 = (1/2)(360/t - 20) mph

v2 = 20 + (1/2)(360/t - 20) mph

the speed of the first train is: (1/2)(360/t - 20) mph

the speed of the second train is: 20 + (1/2)(360/t - 20) mph

where t is the time of the travel for each train.