Atrain averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains. if a trip of 300 miles took 3 hour and 48 minutes, how many miles of it was through the mountains?

Let p and m represent the numbers of miles in the plains and mountains, respectively.
.. p + m = 300 . . . . . . . the whole trip was 300 miles

time = distance/speed, so the trip time can be written as
.. p/90 + m/37.5 = 3 48/60
.. 5p + 12m = 1710 . . . . . . . . . . multiply by 450 to put in standard form

You can solve these two equations by any of several means. The variable p can be eliminated by subtracting 5 times the first from the second.
.. (5p +12m) -5(p +m) = 1710 -5*300
.. 7m = 210
.. m = 30

30 miles of the trip was through the mountains.