SOLUTION: an express train takes 1.5 hour less that a passenger train to travel 180 km distance. the speed of the express train is 20 km/hr more than passenger train. find speed of both trai

Question 930282: an express train takes 1.5 hour less that a passenger train to travel 180 km distance. the speed of the express train is 20 km/hr more than passenger train. find speed of both trains?

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = speed of express train
y = speed of passenger train
t = time of passenger train
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s = d/t
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express train:
x = 180/(t - 1.5)
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passenger train:
y = 180/t
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x = y + 20
180/(t - 1.5) = 180/t + 20
180/(t - 1.5) - 180/t = 20
180t/t(t - 1.5) - 180(t - 1.5)/t(t - 1.5) = 20
180t - 180(t - 1.5)= 20t(t - 1.5)
180t - 180t + 1.5*180 = 20tt - 1.5*20t
20tt - 1.5*20t - 1.5*180 = 0
tt - 1.5t - 13.5 = 0
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the above quadratic equation is in standard form, with a=1, b=-1.5 and c=-13.5
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -1.5 -13.5
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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t = 4.5
t = -3
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the negative root doesn't fit the problem statement, so use the positive root:
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t = 4.5
x = 180/(t - 1.5)
x = 180/(4.5 - 1.5)
x = 60
y = 180/t
y = 180/4.5
y = 40
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answer:
x = speed of express train = 60 kph
y = speed of passenger train = 40 kph
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---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
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