Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - Problem Solving - Page 39: 7

Answer

$$T=\frac{\sqrt{x^2+4}}{2}+\frac{\sqrt{x^2-6x+10}}{4}$$

Work Step by Step

As we know, the time needed to travel $\Delta x$ at the speed $v$ is $\Delta T = \frac{\Delta x}{v}$. So, the only things needed to be calculated are the distance $\Delta x_1$ traveled by rowing and the distance $\Delta x_2$ traveled by walking. According to the figure, by applying the Pythagorean Theorem we obtain$$\Delta x_1=\sqrt{x^2+2^2}= \sqrt{x^2+4} \\ \Delta x_2= \sqrt{(3-x)^2+1^2}= \sqrt{x^2-6x+10} \, .$$Thus, the total time of the trip is$$T=\Delta T_1+\Delta T_2=\frac{\Delta x_1}{v_1}+ \frac{\Delta x_2}{v_2}= \frac{\sqrt{x^2+4}}{2}+\frac{\sqrt{x^2-6x+10}}{4} \, .$$
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