SOLUTION: A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 12 miles per hour faster than the southbou

Let x be the speed of the slower speed train, in miles per hour.

Then the speed of the faster train is  (x+12) mph.


In 1.5 hours, the slower train covered the distance of 1.5*x miles,

while the faster train covered the distance of 1.5*(x+12) miles.


Since they travel in opposite directions, the full distance between them is the sum of partial distances.


    1.5x + 1.5*(x+12) = 177.


    1.5x + 1.5x + 18 = 177


    3x = 177 - 18 = 159  ====>  x = 159/3 = 53.


Answer.  The trains travel at 53 and 65 miles per hour.