SOLUTION: Larry's time to travel 312 miles is 3 hours more than Terrell's time to travel 162 miles. Terrell drove 2 miles per hour faster than Larry. How fast did each one travel?

Question 932559: Larry's time to travel 312 miles is 3 hours more than Terrell's time to travel 162 miles. Terrell drove 2 miles per hour faster than Larry. How fast did each one travel?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = larry speed
y = terrell speed
t = terrell time
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s = d/t
t = d/s
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larry time:
t + 3 = 312/x
t = 312/x - 3
---
terrell time:
t = 162/y
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y = x + 2
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equate times:
312/x - 3 = 162/y
312/x - 3 = 162/(x + 2)
312/x - 162/(x + 2) = 3
312(x + 2)/x(x + 2) - 162x/x(x + 2) = 3
312(x + 2) - 162x = 3x(x + 2)
312x + 312*2 - 162x = 3xx + 6x
150x + 624 = 3xx + 6x
3xx - 144x - 624 = 0
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the above quadratic equation is in standard form, with a=3, b=-144 and c=-624
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
3 -144 -624
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
---
x = 52
x = -4
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the negative root doesn't fit the problem statement, so use the positive root:
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answer:
x = larry speed = 52 mph
y = terrell speed = 54 mph
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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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