SOLUTION: 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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 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       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
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.