SOLUTION: It takes a freight train 2 hrs longer to travel 300 miles than it takes an express train to travel 280 miles. The rate of the express train is 20 miles per hour greater than the ra

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Question 36026: It takes a freight train 2 hrs longer to travel 300 miles than it takes an express train to travel 280 miles. The rate of the express train is 20 miles per hour greater than the rate of the freight train. Find the times and rates of both trains.

Found 2 solutions by Paul, stanbon:
Answer by Paul(988) (Show Source):
You can put this solution on YOUR website!
The ffreight train travels at x mph
The express train travels at 20+x mph
Equation:

300(x+20)-280(x)=2[(x)(x+20)]
20x+6000=2(x^2+20x)
2x^2+40x-20x-6000=0
x^2+10x-3000=0
Can you solve that you get x=50
50+20=70
Hence, the speed of the freight train is 50mph and the speed of the express train is 70mph.
Paul.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
It takes a freight train 2 hrs longer to travel 300 miles than it takes an express train to travel 280 miles. The rate of the express train is 20 miles per hour greater than the rate of the freight train. Find the times and rates of both trains.
Freight train Data:
distance=300 miles; time=x+2 hrs rate=300/(x+2) mph
Express train Data:
distance=280; time=x hrs; rate=280/x mph
EQUATION:
rate of express train = rate of freight train + 20
280/x = 300/(x+2) + 20
Multiply through by x(x+2)
280(x+2)=300x + 20x(x+2)
280x+560 = 300x+20x^2+40x
20x^2+60x-560=0
Divide thru by "20" to get:
x^2+3x-28=0
(x+7)(x-4)=0
x=4 hrs (time for the express train)
280/x=70mph (rate of the express train)
x+2=6 hrs (time for the freight train)
300/(x+2)=300/6=50 mph (rate of the freight train)
Cheers,
Stan H.