Chapter 7.1, Problem 52E

Solution

To calculate: The airplane speed and the wind speed.

The airplane speed and the wind speed are 617.43 mi/hr and 49.25 mi/hr.

Given Information:

The distance between Los angles and New York is 2500 mi. The time taken against the wind is 4.4 hr and with wind is 3.75 hr.

Calculation:

Consider the given information,

Suppose that the airplane speed and the wind speed be $x$ and $y$ respectively.

The time taken against the wind is 4.4 hr and with wind is 3.75 hr. It implies,

  $\begin{array}{c}\frac{2500}{x-y}=4.4\\ x-y=666.67\end{array}$   .....,. (1)

And,

  $\begin{array}{l}\frac{2500}{x+y}=3.75\\ x+y=568.18\end{array}$   .....,. (2)

Adding equation (1) and (2),

  $\begin{array}{c}2x=666.67+568.18\\ x=617.43\text{ mi/hr}\end{array}$

Substitute $x$ in equation (1),

  $\begin{array}{c}617.43-y=666.67\\ y=49.25\text{ mi/hr}\end{array}$

Therefore, the airplane speed and the wind speed are 617.43 mi/hr and 49.25 mi/hr.