SOLUTION: It takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. The rate of the express is 20 miles per hour faster than the rate of t

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Question 407634: It takes a freight train 3 hours more to travel 200 miles than it takes an express train to travel 120 miles. The rate of the express is 20 miles per hour faster than the rate of the freight train. How do I find the rates of both trains.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"The rate of the express is 20 miles per hour faster than the rate of the freight train"
___ e = f + 20

t = d / r ___ the freight train time is 3 hr longer

(200 / f) - 3 = 120 / e

substituting ___ (200 / f) - 3 = [120 / (f + 20)]

multiplying by [f(f+20)] ___ 200(f+20) - 3[f(f+20)] = 120(f)

200f + 4000 - 3f^2 - 60f = 120f ___ 0 = 3f^2 - 20f - 4000

factoring ___ 0 = (3f + 100)(f - 40)

3f + 100 = 0 ___ f = -100/3 ___ negative value not realistic

f - 40 = 0 ___ f = 40 ___ substitute back to find e