Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.7 - Formulas and Applications of Rational Equations - Exercise Set - Page 476: 35


$12$ miles

Work Step by Step

distance = (rate)$\times$(time) $\Rightarrow$ time = $\displaystyle \frac{\text{distance}}{\text{rate}}$ We are given:$\quad t_{2}=t_{1}+0.5$ (in hours), where the indices 1 and 2 represent runners 1 and 2. The time $t_{1}$ is shorter for the faster runner (runner 1) Let d be the distance (length of the trail). $\displaystyle \frac{d}{6}=\frac{d}{8}+\frac{1}{2}\qquad $.../$\times$LCD= 24 $4d=3d+12\qquad.../-3d$ $d=12$ miles
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