Question 295938
A bullet train travels 30 mph faster than a passenger train, and it takes the bullet train 3 hours less time to travel 400 miles. How long does it take the passenger train to make the trip. 
let rate of the passenger train be x mph 
the rate of the bullet train = x+ 30 mph 
Distance = 400 miles 
time taken by passenger train = 400 / x 
time taken by bullet train = 400 / x+30
This takes 3 hours less. 
400/x+30 +3 = 400/x 
400/x+30 -400/x =-3 
400x -400(x+30) = -3x(x+30) 
400x-400x-12000 = -3x^2-90x 
3x^2+90x-12000 =0 
x^2+30x-4000=0 
x^2+80x-50x-4000=0 
x(x+80)-50(x+80)=0 
(x-50)(x+80)=0 
x=50 the rate of the passenger train 
It takes 8 hours to make the trip of 400 miles.