Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Section 4.3 - Systems of Linear Equations and Problem Solving - Exercise Set - Page 231: 19

Answer

The wind speed is 90 mph, and the plane speed is 630 mph.

Work Step by Step

We assume that the actual speed of the plane is equal to the wind speed plus the speed the plane would fly if there was no wind at all. We use the equation speed is equal to change in distance divided by change in time to find: $w+p = 2160/3$ and $p-w = 2160/4$ We add the two equations to find: $2p = 2160/3 + 2160/4$ Now, we use PEMDAS, a method for simplification. This acronym reminds us that we must first address parentheses, and then exponents. Next, we address multiplication and division, going from left to right. Lastly, we simplify addition and subtraction from left to right. This gives: $ p = 630 mpg$ We substitute back into the original equation to find that the wind speed is: $ 90 mph$
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