SOLUTION: A freight train covered 120 miles at a certain speed. Had the train been able to travel 10 mph faster, the trip would have been 2 hours shorter. How fast did the train go?

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Question 718412: A freight train covered 120 miles at a certain speed. Had the train been able to travel 10 mph faster, the trip would have been 2 hours shorter. How fast did the train go?
Found 2 solutions by lynnlo, Edwin McCravy:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A freight train covered 120 miles at a certain speed. Had the train been able to travel 10 mph faster, the trip would have been 2 hours shorter. How fast did the train go?

That other "tutor" is only showing his ignorance of algebra.

Make this chart:
                     Distance    Rate   Time
Trip that happened      120        x     t     
Trip that didn't        120      x+10   t-2

Use DISTANCE = RATE × TIME, we get this system
from the chart:

         120 = xt
         120 = (x+10)(t-2)

Since they're both equal to 120, set them equal

          xt = (x+10)(t-2)

Multiply out the right side

          xt = xt-2x+10t-20

Subtract xt from both sides:

           0 = -2x+10t-20

          2x = 10t-20

Divide through by 2

           x = 5t-10

Substitute 5t-10 for x in

         120 = xt

         120 = (5t-10)t

         120 = 5t²-10t

-5t²+10t+120 = 0

Divide through by -5

    t²-2t-24 = 0

  (t-6)(t+4) = 0

t-6 = 0;   t+4 = 0
  t = 6;     t = -4 (ignore)
  x = 5t-10
  x = 5(6)-10
  x = 30-10
  x = 20

The train went 20 mph

Edwin