Question 829373: James took 1h more than John to drive a 432-mi trip at an average speed of 6mi/h less than John. How fast did they each drive?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
x = James' speed
y = John's speed
t = John's time
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s = d/t
d = s*t
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James' distance:
432 = (y - 6)(t + 1)
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John's speed:
y = 432/t
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John's distance:
432 = yt
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432 = 432
(y - 6)(t + 1) = yt
yt + y - 6t - 6 = yt
y = 6t + 6
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y = 432/t
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432/t = 6t + 6
6tt + 6t - 432 = 0
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the above quadratic equation is in standard form, with a=6, b=6, and c=-432
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
6 6 -432
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 = 8
t = -9
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negative time doesn't fit the problem statement, so use the positive root:
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John's time = 8 hours
James' time = 9 hours
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answer:
John's speed = 432/8 = 54 mph
James' speed = 432/9 = 48 mph
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