A freight train takes 2 hours longer to travel 300 miles tha

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!

Solution

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