SOLUTION: It takes a freight train 3 hours more to travel 280 miles than it takes an express train to travel 200 miles. The rate of the express is 10 miles per hour faster the the rate of t

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Question 426400: It takes a freight train 3 hours more to travel 280 miles than it takes an express train to travel 200 miles. The rate of the express is 10 miles per hour faster the the rate of the freight train. Fine the rates of both trains.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Freight train x mph 280 miles
Express train x +10 mph 200 miles

t=d/r
280/x=200/(x+10)+3
280/x-200 /(x+10)=3
LCD = x(x+10)
Multiply by LCD
280(x+10)-200x=3x(x+10)
280x+2800-200*x =3x^2+30
3X^2+80x-2770=0
Find the roots of the equation by quadratic formula
a=3 b=80 c=-2770
b^2-4ac=6400+33240
b^2-4ac=39640
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=(-80 +199.1)/6
x1=19.85
x2=(-80 -199.1)/6
x2= -46.52
Ignore negative value
x=19.85 mph Freight train speed
29.85 mph=Express train speed