Elementary Algebra

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

Chapter 7 - Algebraic Fractions - 7.6 - More Fractional Equations and Problem Solving - Problem Set 7.6: 46

Answer

It will take Pam 2 hours and Laura 6 hours.

Work Step by Step

Let t be the time it takes Pam. Thus: $ 1/ 1.5 = \frac{1}{t} + \frac{1}{t+4} $ We create common denominators to obtain: $ .67 = \frac{t+t+4}{t(t+4)} \\ .67t^2 + 2.67t = 2t +4 \\ .67t^2 +.67t -4 = 0 \\ t^2 +t -6 = 0 \\(t+3)(t-2) =0$ Since t can't be negative, we see that it takes Pam 2 hours. This means it takes Laura 2+4 = 6 hours.
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