SOLUTION: It takes a freight train 2 hours longer to travel 200 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

Question 94285: It takes a freight train 2 hours longer to travel 200 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.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
It takes a freight train 2 hours longer to travel 200 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.
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Freight train DATA:
Time = x+2 hrs ; distance = 200 miles; rate = d/t = 200/(x+2)
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Express train DATA:
Time = x hrs ; distance = 280 miles; rate = d/t 280/x
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EQUATION:
express rate = freight rate + 20
280/x = 200/(x+2) + 20
Divide thru by 20 to get:
14/x = 10/(x+2) + 1
Multiply thru by x(x+2) to get:
14(x+2) = 10x + x(x+2)
14x+28 = 10x + x^2+2x
x^2-2x-28 = 0
x = [2+-sqrt(4-4*-28)]/2
x = [2 +- sqrt(116)]/2
x = [1 +- sqrt(29)]
Positive answer:
x = 1+sqrt29 = 6.39 = 6 hrs 23 minutes (time for the express train)
280/x = 43.85 mph (rate of the express train}
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x+2 = 8 hrs 23 minutes (time for the freight train)
200/(x+2) = 23.85 mph (rate of the freight train)

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Cheers,
Stan H.

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