SOLUTION: Carlos takes 20 minutes longer than erica does to make the 342 mile drive between two cities. erica drives 3 miles per hour faster than carlos. how fast do carlos and erica drive?

Question 930537: Carlos takes 20 minutes longer than erica does to make the 342 mile drive between two cities. erica drives 3 miles per hour faster than carlos. how fast do carlos and erica drive?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = carlos speed
y = erica speed = x + 3
t = erica time
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s = d/t
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carlos:
x = 342/(t + 20/60)
x = 342/(t + 1/3)
---
erica:
y = 342/t
x + 3 = 342/t
x = 342/t - 3
---
equate x's:
342/(t + 1/3) = 342/t - 3
342/(t + 1/3) - 342/t = -3
342t/t(t + 1/3) - 342(t + 1/3)/t(t + 1/3) = -3
342t - 342(t + 1/3) = -3t(t + 1/3)
342t - 342t - 342/3 = -3tt - 3t/3
-3tt - 3t/3 + 342/3 = 0
tt + t/3 - 342/9 = 0
tt + 0.333333333t - 38 = 0
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the above quadratic equation is in standard form, with a=1, b=0.333333333 and c=-38
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 0.333333 -38
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
---
t = 6
t = -6.33333333
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the negative root doesn't fit the problem statement, so use the positive root:
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t = 6
x = 342/(t + 1/3)
x = 342/(6 + 1/3)
x = 54
y = 342/t
y = 342/6
y = 57
---
answer:
x = 54 mph
y = 57 mph
---
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---
Solve quadratic equations, quadratic formula:
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---
Solve systems of linear equations up to 6-equations 6-variables:
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