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?
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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
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Time for bullet train to travel 400 miles:
since t = d/r
400/(P+30)
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Time for passenger train to travel 400 miles:
since t = d/r
400/P
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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
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So, time it takes to travel 400 miles:
400/50 = 8 hours