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: 67

Answer

Irene: 3h Henry: 4.5h

Work Step by Step

It takes Irene x hours to finish work It takes Henry x+1.5h (x+$\frac{3}{2}$h) to finish work It takes them 1h 48minutes (1h +$\frac{4}{5}$h) to finish work together Fractions of work they do in an hour: Irene: $\frac{1}{x}$ Henry: $\frac{1}{x+\frac{3}{2}}$ Together: $\frac{1}{1+\frac{4}{5}}$ Equation: $\frac{1}{1+\frac{4}{5}}$= $\frac{1}{x}$+$\frac{1}{x+\frac{3}{2}}$ $\frac{5}{9}$= $\frac{1}{x}$+$\frac{2}{2x+3}$ multiply by 9x(2x+3) 5x(2x+3)=9(2x+3)+18x 10$x^{2}$+15x=18x+27+18x 10$x^{2}$-21x-27=0 Quadtratic formula: 441-4$\times$10$\times$(-27)=1521 x=$\frac{21+or-\sqrt1521}{20}$ Time must be positive so the only answer is x=3
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