Two trains leave a town at the same time heading in opposite directions. one train is traveling 12 mph faster than the other after two hours, they are 232 miles apart. what is the average speech of each train ?

52; 64
So the train is going the opposite direction so the two train add to 232 which is model by this formula:
x+12 = y
2(y+x) = 232
so the x is the slower train mph and the y is the faster train mph, you can substitute y with x+12:
2((x+12)+x) = 232
2(2x+12) = 232
4x + 24 = 232
4x + 24 = 232 - 24
4x = 208
4x/4 = 208/4
x = 52
52 + 12 = y
y = 64
so the slower train is 52 and the faster train is 64