Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.2 Applications and Modeling with Linear Equations - 1.2 Exercises - Page 102: 26

Answer

$1hr 6 mins 47 secs$ is the time of Usain Bolt if he would run for an entire 26 mile marathon with his 2009 new world record time. If to compare with the fastest time for the 26 mile marathon, which is $2 hrs 3 mins 23 secs$ set in 2013, Usain Bolt could have won the record with an ahead time of approximately $56 mins 36 secs.$

Work Step by Step

Bolt's average speed in meters per second is $speed=\frac{d}{t}$ $speed=\frac{100}{9.58}$ $speed≈10.44 m/s$ Convert the marathon distance to meters 26 miles to meters: $26×5280ft×\frac{1m}{3.281ft}$ $≈41840.9 m$ The time needed to cover this distance at average speed of 10.44 m/s is $t=41840.9÷10.44\approx4007.75 seconds$ $=4007.75÷3600≈1.113 hours$ $=1 hour + 0.113(60)min =1h 6.78 min$ $=1h 6 min +0.78(60) s$ $≈1h 6min 47sec$ 1hr 6 mins 47 secs is the time of Usain Bolt if he would run for an entire 26 mile marathon with his 2009 new world record time. If to compare with the fastest time for the 26 mile marathon, which is 2 hrs 3 mins 23 secs set in 2013, Usain Bolt could have won the record with an ahead time of approximately 56 minutes and 36 seconds.
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