Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 3 - Equations and Problem Solving - 3.5 - Problem Solving - Problem Set 3.5: 20

Answer

It will take Nancy 1.25 hours to overtake Kirk.

Work Step by Step

Let t represent the time it will take Nancy to catch Kirk. Since Kirk starts jogging half an hour earlier, he jogs for t+0.5. Kirk jogs at 5 miles per hour, so he jogs for a distance equal to (t + 0.5) $\times$ 5 = 5t + 2.5 Nancy jogs at 7 miles per hour, which means that she travels for a distance equal to t $\times$ 7 = 7t. Because Nancy is to overtake Kirk, the distances must be equal. So: 5t + 2.5 = 7t 2t = 2.5 Divide both sides by 2. t = 1.25 It will take Nancy 1.25 hours to overtake Kirk.
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