SOLUTION: A freight train takes 2 hours longer to travel 300 miles than an express train to travel 280 miles. The rate of the express train is 20mph greater than the rate of the freight trai

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Question 151407: A freight train takes 2 hours longer to travel 300 miles than an express train to travel 280 miles. The rate of the express train is 20mph greater than the rate of the freight train. Find the time for the express train.
Please help!
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
300=r(t+2)
r=300/(t+2)
280=(r+20)t
280=(300/(t+2)+20)t
280=300t/(t+2)+20t
280=(300t+20t(t+2))/(t+2)
280(t+2)=300t+20t^2+40t
280t+560=340t+20t^2
20t^2+340t-280t-560=0
20t^2+60t-560=0
20(t^2+3t-28)=0
20(t+7)(t-4)=0
t-4=0
t=4 hours for the express train
280=4(r+20)
280=4r+80
4r=280-80
4r=200
r=200/4
r=50 mph is the rate of the freight train.
proofs:
300=50(4+2)
300=300
280=(50+20)*4
280=70*4
280=280