Chapter 7.2, Problem 77E

To determine

To calculate : The airspeed of the airplane and the speed of the wind.

Answer to Problem 77E

The airspeed of the airplane and the speed of the windare $550\text{ mile per hour}$ and $50\text{ mile per hour}$ respectively.

Explanation of Solution

Given information :

Total distance covered by the airplane between New York city and Albuquerque $=1800\text{ mile}$

Time take by the airplane to travel between New York city and Albuquerque

  $\begin{array}{c}\text{Time}\text{Taken}=3\text{ hours }36\text{ minutes}\\ =\left(3+\frac{36}{60}\right)\text{ hours}\\ =\left(3+\frac{6}{10}\right)\text{ hours}\\ =3.6\text{ hours}\end{array}$

Time take by the airplane to travel betweenAlbuquerque and New York city

  $=3\text{ hours}$

Calculation :

Suppose the airspeed of the airplane be $x$ miles per hour and the speed of the wind be $y$ miles per hour.

Assuming the wind is blowing from Albuquerque and New York city. The direction of wind will remain constant.

Since, the airplane is flying from New York city to Albuquerque, the net speed of airplane is calculated as $\left(x-y\right)\text{ miles per hour}$ .

Now, according to the question:

  $\begin{array}{l}\text{Speed = }\frac{\text{Total distance covered}}{\text{Total time taken}}\\ \left(x-y\right)=\frac{1800}{3.6}\end{array}$

  $x-y=500$  ...(1)

Similarly, the airplane is flying from Albuquerque to New York city, the net speed of airplane is calculated as $\left(x+y\right)\text{ miles per hour}$ .

  $\begin{array}{l}\text{Speed = }\frac{\text{Total distance covered}}{\text{Total time taken}}\\ \left(x+y\right)=\frac{1800}{3}\end{array}$

  $x+y=600$  ...(2)

Solve equation (1) and (2):

  $\underset{\_}{\begin{array}{l}x-\cancel{y}=500\\ \text{+ }x+\cancel{y}=600\end{array}}$

  $\begin{array}{l}2x=1100\\ x=\frac{1100}{2}\\ x=550\end{array}$

Calculate value of $y$ by putting value of $x$ in equation (1):

  $\begin{array}{l}x-y=500\\ y=x-500\\ y=550-500\\ y=50\end{array}$

Therefore, the airspeed of the airplane and the speed of the windare $550\text{ mile per hour}$ and $50\text{ mile per hour}$ respectively.