University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 59



Work Step by Step

$\mathrm{Given:}\:\:\:$ The variable $\:s\:$ is proportional to $\:t.$ We can write the above statement as a relation: $s\:\propto\:t$ Let's introdue a proportionality constant $\:k\:$ to turn the relation into an equation as: $s=k\cdot t$ We can find the value of $\:k\:$ when we are given $\:s=25\:$ and $\:t=75.$ $25=k\cdot 75$ $\Rightarrow\: k=\frac{25}{75}=\frac{1}{3}$ So that our general equation $\:s=k\cdot t\:$ becomes: $s=\frac{1}{3}\cdot t$ When $\:s=60,\:$ we have: $60=\frac{1}{3}\cdot t$ $\Rightarrow\: t=60\cdot 3$ $\Rightarrow\: t=180$
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