Question 251327
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Let *[tex \Large r_S] represent her speed in still water and let *[tex \Large r_c] represent the speed of the current.


Since we know that distance equals rate times time, 20 minutes is one-third of an hour, 9 minutes is 3/20ths of an hour, her speed relative to dry land upstream (against the current) must be *[tex \Large r_S\ -\ r_c], and the speed downstream must be *[tex \Large r_S\ +\ r_c], we can say the following things:


With respect to the upstream trip:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \left(r_S\ -\ r_c\right)\left(\frac{1}{3}\right)\ =\ 1]


And with respect to the downstream trip:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \left(r_S\ +\ r_c\right)\left(\frac{3}{20}\right)\ =\ 1]


A little arithmetic:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  r_S\ -\ r_c\ =\ 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  r_S\ +\ r_c\ =\ \frac{20}{3}]


Now all you need to do is solve the linear system.  The coordinates of the single ordered pair in the solution set are the answers you seek.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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