It takes a freight train 2 hrs longer to travel 300 miles th

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.

Solution

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)