## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Review Exercises - Page 877: 11

#### Answer

The average velocity of the plane is $630\text{ mph}$ and the average velocity of the wind is $90\text{ mph}$.

#### Work Step by Step

Consider the average velocity of the plane to be $x$ and the average velocity of the wind to be $y$. The average velocity of the plane in the direction of the wind is $x+y$ and the average velocity against the wind is $x-y$. A plane takes $3$ hours to fly $2160$ miles in the direction of the wind and it takes $4$ hours to fly the same distance against the direction of the wind. Form the equations in the table: \begin{align} & 3\left( x+y \right)=2160 \\ & x+y=720 \end{align} …… (1) And \begin{align} & 4\left( x-y \right)=2160 \\ & x-y=540 \end{align} …… (2) Add equation (1) and equation (2). \begin{align} & \underline{\begin{align} & x+y=720 \\ & x-y=540 \end{align}} \\ & 2x\text{ }=1260 \\ & \text{ }x\text{ }=630 \\ \end{align} Substitute $x=630$ in equation (1). \begin{align} & x+y=720 \\ & 630+y=720 \\ & y=720-630 \\ & y=90 \end{align} Therefore, the average velocity of the plane is $630\text{ mph}$ and the average velocity of the wind is $90\text{ mph}$.

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