College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.4 - Solving Quadratic Equations - 1.4 Exercises - Page 124: 81

Answer

$6$ km/h

Work Step by Step

Let's note by $x$ the rowing speed in still water. The rowing speed upstream is diminished by the rate of the flow, while the rowing speed downstream is increased by the rate of the flow. We write the equation for the total time and solve it for $x$: $$\begin{align*} \dfrac{6}{x-3}+\dfrac{6}{x+3}&=2\dfrac{40}{60}\\ \dfrac{6}{x-3}+\dfrac{6}{x+3}&=\dfrac{8}{3}\\ 18(x+3)+18(x-3)&=8(x+3)(x-3)\\ 18x+54+18x-54&=8(x^2-9)\\ 36x&=8x^2-72\\ 8x^2-36x-72&=0\\ 4(2x^2-9x-18)&=0\\ 2x^2-9x-18&=0\\ x&=\dfrac{-(-9)\pm\sqrt{(-9)^2-4(2)(-18)}}{2(2)}\\ &=\dfrac{9\pm 15}{4}\\ x_1&=\dfrac{9-15}{4}=-\dfrac{3}{2}\\ x_2&=\dfrac{9+15}{4}=6. \end{align*}$$ Because $x>0$, the only solution that fits is $x=6$ km/h.
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