Chapter 9.6, Problem 15P

To determine

Tofind:The speed of the plane in still air and the speed of the wind.

Answer to Problem 15P

The rate at still air is $\text{770}\text{km}/\text{h}$ and the rate of the wind is $\text{70}\text{km}/\text{h}$ .

Explanation of Solution

Given:

The $4200$ km trip from New York to san Francisco takes $6$ hours against the wind.

In return it took only $5$ hours.

Concept used:

Speed and the rate here has same meaning.

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

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:

  $\text{distance=rate×time}$ .

  $\text{4200=}\left(\text{r+w}\right)\left(5\right)$ .

Dividing both side by $\text{5}$ :

  $\text{r+w}=840$ ………………. $\left(\text{i}\right)$

Similarly,

  $\text{4200=}\left(\text{r-w}\right)\left(6\right)$ .

  $\text{r-w}=700$ ……………….. $\left(\text{ii}\right)$

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

  $\text{r=770}$ and $\text{w=70}$ .

Hence, the rate at still air is $\text{770}\text{km}/\text{h}$ and the rate of the wind is $\text{70}\text{km}/\text{h}$ .