Question 821599: [ A boat travels 25 mph is still water. it takes 3 1/3 hrs 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? ]
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
s = d / t
t = d / s
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T = 3+1/3 = 10/3 = 40/(25 + w) + 40/(25 - w)
10/3 = 40/(25 + w) + 40/(25 - w)
10/3 = 40(25 - w)/(25 - w)(25 + w) + 40(25 + w)/(25 - w)(25 + w)
(10/3)(25 - w)(25 + w) = 40(25 - w) + 40(25 + w)
(250/3 - (10/3)w)(25 + w) = 1000 - 40w + 1000 + 40w
(6250/3) + (250/3)w - (250/3)w - (10/3)ww - 2000 = 0
(6250/3) - (10/3)ww - (6000/3) = 0
-(10/3)ww - (250/3) = 0
-3.333333ww - 83.333333 = 0
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the above quadratic equation is in standard form, with a=-3.333333, b=0, and c=-83.333333
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
-3.333333 0 -83.333333
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has complex root, which are:
w = 0 + (-5.00000024)i
w = 0 - (-5.00000024)i
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answer:
this problem has no real solution, which probably means that the problem statement contains one or more errors
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