Chapter 9.7, Problem 1ST

To determine

To solve: the system of equations in two variables.

Answer to Problem 1ST

The rate of the jet in still air is $0.78\text{ km/h}$ and the rate of the wind is $0.018\text{ km/h}$ .

Explanation of Solution

Given information:

A jet travels at a rate of 798 mi/h with the wind. Going against the same wind, the jet travels at a rate of 762 mi/h.

Formula used:

  $\text{Rate }\times \text{ Time = Distance}$ .

Step1. The problem asks for the rate of the jet in still air and the rate of the wind.

Step2. Let r = the rate in km/h of the jet in still air .

Let w = the rate in km/h of the wind.

Step3. Use the facts of the problem to write two equations.

Step4. Solve the equations.

Calculation:

Let r = the rate in km/h of the jet in still air .

Let w = the rate in km/h of the wind.

With the wind	$0.798\text{km/h}$
Against the wind	$0.762\text{km/h}$

According to the equation,

  $\begin{array}{l}=r+w=0.798\\ =r-w=0.762\end{array}$

Adding both the equations we get,

  $\begin{array}{l}=2r=1.56\\ =\frac{2r}{2}=\frac{1.56}{2}\\ =r=0.78\text{ km/h}\end{array}$

Subtracting the equations we get,

  $\begin{array}{l}=2w=0.036\\ =\frac{2w}{2}=\frac{0.036}{2}\\ =w=0.018\text{ km/h}\end{array}$

Hence, the rate of the jet in still air is $0.78\text{ km/h}$ and the rate of the wind is $0.018\text{ km/h}$ .