SOLUTION: Zach paddled a canoe 2 miles upstream in a river that has a current of 3 mph. He then turned around and paddled downstream until he reached his original starting place. If the enti

Question 928034: Zach paddled a canoe 2 miles upstream in a river that has a current of 3 mph. He then turned around and paddled downstream until he reached his original starting place. If the entire trip took him 7 hours, how fast would Zach paddle in still water?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = zach's speed in still water
y = speed of current = 3 mph
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s = d/t
t = d/s
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upstream:
a = time upstream
a = 2/(x - y)
a = 2/(x - 3)
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downstream:
b = time downstream
b = 2/(x + y)
b = 2/(x + 3)
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a + b = 7
2/(x - 3) + 2/(x + 3) = 7
2(x + 3)/(x - 3)(x + 3) + 2(x - 3)/(x - 3)(x + 3) = 7
2(x + 3) + 2(x - 3) = 7(x - 3)(x + 3)
2x + 6 + 2x - 6 = 7(xx - 9)
4x = 7xx - 63
7xx - 4x - 63 = 0
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the above quadratic equation is in standard form, with a=7, b=-4 and c=-63
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
7 -4 -63
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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x = 3.29928902
x = -2.72786044
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the negative root doesn't fit the problem statement, so use the positive root:
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answer:
x = zach's speed in still water = 3.3 mph
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---
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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