Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.7 - Modeling with Equations - 1.7 Exercises - Page 78: 72

Answer

55mph

Work Step by Step

Car #1 needs to pass Car#2 covering the distance of both vehicles. Car #1 is 14ft and Car #2 is 30ft. So with Car#2 moving at 55mph, how fast does Car#1 have to go to make that distance in 6 seconds? Lets start with converting the 50mph to ft/sec. 5280 = feet in a mile $5280*50 = 264000$ft per hour $\frac{264000}{60} = 4400$ft per minute $\frac{4400}{60} = 73\frac{1}{3}$ ft per second So we need to add an additional 44ft per 6 seconds. $\frac{44}{6} = 7\frac{1}{3}$ $ 7\frac{1}{3} + 73\frac{1}{3} = 80\frac{2}{3}$ Then we convert back to mph. $80\frac{2}{3} * 60 = 4840$ft per min $4840 * 60 = 290400$ft per hour $\frac{290400}{5280} = 55$mph
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