Question 295141
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.