Elementary Algebra

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

Chapter 3 - Equations and Problem Solving - Chapter 3 Test: 23

Answer

The second car will overtake the first car after 10 hours.

Work Step by Step

Let t represent the time it will take the second car to overtake the first car. Since the second car travels for t time and leaves one hour later than the first car, it means that the first car travels for one hour more, which is equal to t + 1. For the second car to overtake the first car, it should cover the same distance as the first car. The first car travels at 50 miles per hour, for t+1 hours and for a distance of 50 $\times$ (t + 1) = 50t + 50. The second car travels at 55 miles per hour, for t hours and for a distance of 55 $\times$ t = 55t. Since the distance both cars cover is equal, we solve the following equation: 50t + 50 = 55t 50 = 55t - 50t 50 = 5t Divide both sides by 5: t = 10. The second car will overtake the first car after 10 hours.
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