Question 823236: How in the world do you set this guy up?
A boat travels 25 miles per hour in still water. It takes 3 and 1/3 hours in total for the boat to travel 40 miles up a river and then return by the same route. What is the speed of the current in the river?
Think you guys could help me set it up?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
s = d / t
t = d / s
T = 40/(25 - w) + 40/(25 + w)
T = 40(25 + w)/(25 - w)(25 + w) + 40(25 - w)/(25 - w)(25 + w)
T(25 - w)(25 + w) = 40(25 + w) + 40(25 - w)
T(625 - ww) = 1000 + 40w + 1000 - 40w
T(625 - ww) = 2000
625 - ww = 2000/T
T = 3+1/3 = 10/3
625 - ww = 2000/(10/3)
-ww + 625 = 600
-ww + 25 = 0
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the above quadratic equation is in standard form, with a=-1, b=0, and c=25
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-1 0 25
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
w = -5
w = 5
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negative speed doesn't make sense for this problem, so use the positive root
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answer:
the speed of the current in the river is 5 mph
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Solve quadratic equations, quadratic formula:
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