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: 76

Answer

9mph

Work Step by Step

We first have to make a formula. One boat went speed X for 2 hours so we have $2x$ and the other went an additional 3 for 2 hours so we have $2(x+3)$. and the distance between them, the hypotenuse of the triangle is $30$ miles. So we will use the Pythagorean Theorem to build our formula. $A^2+B^2 = C^2$ $(2x)^2+(2(x+3))^2 = 30^2$ $4x^2+(2x+6)^2 = 900$ $4x^2+4x^2+24x+36 = 900$ $4x^2+4x^2+24x+36 = 900$ $8x^2+24x+36 = 900$ Now let's move everything over to one side so we can use the quadratic formula: $8x^2+24x-864 = 0$ Great then we just plug this into the quadratic formula for the answer: $x = \frac{-24\frac{+}{-}\sqrt (24^2-(4*8*-864))}{2*8}$ $x = \frac{-24\frac{+}{-}\sqrt (576-(-27648))}{16}$ $x = \frac{-24\frac{+}{-}\sqrt (28224)}{16}$ $x = \frac{-24\frac{+}{-}168}{16}$ so we get our two answers: $x = \frac{-192}{16}$ = -12 and $x = \frac{144}{16}$ = 9 We know that we have to have a positive number for this problem so our answer is 9.
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