SOLUTION: A bullet train travels 30 miles per hour faster than a passenger train, and it takes the bullet train 3 hours less time to travel 400 miles. How long does it takes the passenger tr
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Question 295938: A bullet train travels 30 miles per hour faster than a passenger train, and it takes the bullet train 3 hours less time to travel 400 miles. How long does it takes the passenger train to make the trip?
Found 2 solutions by mananth, nerdybill:
Answer by mananth(16946) (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.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A bullet train travels 30 miles per hour faster than a passenger train, and it takes the bullet train 3 hours less time to travel 400 miles. How long does it takes the passenger train to make the trip?
.
We will be applying the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
Let P = speed of passenger train
then
P+30 = speed of bullet train
.
Time for bullet train to travel 400 miles:
since t = d/r
400/(P+30)
.
Time for passenger train to travel 400 miles:
since t = d/r
400/P
.
From: "it takes the bullet train 3 hours less time to travel 400 miles."
we get our equation:
400/(P+30) = 400/P - 3
multiply both sides by P(P+30):
400P = 400(P+30) - 3P(P+30)
400P = 400P+12000 - 3P^2-90P
0 = 12000 - 3P^2-90P
3P^2 + 90P -12000 = 0
P^2 + 30P - 4000 = 0
(P+80)(P-50) = 0
P = {-80, 50}
We can toss out the negative answer leaving us with:
P = 50 mph
.
So, time it takes to travel 400 miles:
400/50 = 8 hours
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