SOLUTION: 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?

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!
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x = James' speed
y = John's speed
t = John's time
---
s = d/t
d = s*t
---
James' distance:
432 = (y - 6)(t + 1)
---
John's speed:
y = 432/t
---
John's distance:
432 = yt
---
432 = 432
(y - 6)(t + 1) = yt
yt + y - 6t - 6 = yt
y = 6t + 6
---
y = 432/t
---
432/t = 6t + 6
6tt + 6t - 432 = 0
---
the above quadratic equation is in standard form, with a=6, b=6, and c=-432
---
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
---
the quadratic has two real roots at:
---
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
---
answer:
John's speed = 432/8 = 54 mph
James' speed = 432/9 = 48 mph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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