SOLUTION: Find the speed of a train if an increase of 6 kph lowers the time for a journey of 72 km by 10 minutes.

Question 816658: Find the speed of a train if an increase of 6 kph lowers the time for a journey of 72 km by 10 minutes.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
s = d / t
d = s * t
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D = 72 = st
D = (s + 6)(t - 1/6)
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st = (s + 6)(t - 1/6)
st = st - (1/6)s + 6t - 1
0 = -(1/6)s + 6t - 1
0t = -(1/6)st + 6tt - t
0 = -(1/6)72 + 6t^2 - t
0 = 6t^2 - t - 12
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the above quadratic equation is in standard form, with a=6, b=-1, and c=-12
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to solve the quadratic equation, plug this:
6 -1 -12
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
t = 1.5
t = -1.33333333
---
negative time doesn't make sense for this problem, so use the positive root:
t = 1.5 hours
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Answer:
the speed of a train: 72 km / 1.5 hours = 48 kph
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Solve quadratic equations, quadratic formula:
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