Chapter 9.6, Problem 11P

To determine

To find: the speed of the plane in still air and the speed of the wind.

Answer to Problem 11P

The rate of plane in still air is $\text{r=1300}\text{km}/\text{h}$ and the rate of the wind is $100\text{km}/\text{h}$ .

Explanation of Solution

Given:

A plane travels $8400$ km flying against the wind in $7$ hours

In return it took only $6$ hours with the winds.

Concept used:

Speed and the rate are same meaning here.

  $\text{Distance=rate}\times \text{time}$ .

In the elimination method:

Either add or subtract equation to get an equation in one variable.

When the coefficients in one variable are opposites then add the equations to eliminate the variable and when the coefficients of one variable are equal and subtract the equation to eliminate a variable.

Calculation:

Let $\text{r}$ be the rate of plane without wind and $\text{w}$ be the rate of the wind.

Then the plane’s rate with the wind is $\text{r+w}$ and against the wind is $\text{r-w}$ .

Using formula:

  $\text{distance=rate×time}$ .

  $\left(\text{r-w}\right)7=8400$ ………. $\left(\text{i}\right)$

  $\left(\text{r+w}\right)6=8400$ ………. $\left(\text{ii}\right)$

Dividing $\left(\text{i}\right)$ equation by $\text{7}$ and $\left(\text{ii}\right)$ equation by $\text{6}$ :

  $\left(\text{r-w}\right)=1200$ ………………. $\left(\text{i}\right)$

Similarly,

  $\left(\text{r+w}\right)=1400$ ……………….. $\left(\text{ii}\right)$

Adding the equation $\left(\text{i}\right)$ and $\left(\text{ii}\right)$

  $\text{r=1300}$ and $\text{w=100}$ .

Hence, the rate of plane in still air is $\text{r=1300}\text{km}/\text{h}$ and the rate of the wind is $100\text{km}/\text{h}$ .