Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Integrated Review - Summary on Solving Quadratic Equations - Page 792: 32

Answer

5.73 mph for 5 miles, 6.73 mph for 2 miles

Work Step by Step

5 miles at a rate of $x$ mph 2 miles at a rate of $x+1$ mph $(5/x) + (2/(x+1)) = 4/3$ $\frac{5}{x} + \frac{2}{x+1} = \frac{4}{3}$ $x*(x+1)*3*\frac{5}{x} + x*(x+1)*3*\frac{2}{x+1} = x*(x+1)*3*\frac{4}{3}$ $\frac{x*(x+1)*3*5}{x} + \frac{x*(x+1)*3*2}{x+1} = \frac{x*(x+1)*3*4}{3}$ $\frac{(x+1)*3*5}{1} + \frac{x*3*2}{1} = \frac{x*(x+1)*4}{1}$ $15(x+1) + 6x = 4x(x+1)$ $15x+15+6x=4x^2+4$ $21x + 15=4x^2+4$ $4x^2+4=21x+15$ $4x^2-21x-11=0$ $x=(-b±\sqrt {b^2-4ac})/2a$ $x=(-(-21)±\sqrt {(-21)^2-4*4*(-11)})/2*4$ $x=(21±\sqrt {441+4*4*(11)})/8$ $x=(21±\sqrt {441+176)})/8$ $x=(21±\sqrt {617})/8$ We want the positive square root since we are talking about time. $x=(21±\sqrt {617})/8$ $x=(21±24.8395)/8$ $x=(21+24.8395)/8$ $x=(45.8395)/8$ $x=5.73$
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