Chapter 7.2, Problem 41E

To determine

To calculate: the air speed of the plane and the wind air speed.

Answer to Problem 41E

The air speed of the plane is 691.3 miles per hour and the speed of the wind is 91.3 miles per hour.

Explanation of Solution

Given information:

Flying distance between Indianapolis, Indiana and Phoenix, Arizona is 1800-mile.

Time taken by the airplane, flying into a headwind, to travel the 1800-mile distance is 3 hours.

Time taken by the airplane to travel the same distance on the return flight is 2 hours 30 minutes.

Formula used:

  $\text{time}\times \text{speed}=\text{distance}$

Calculation:

Let $v_1$ = the air speed of the plane in miles per hour

  $v_2$ = the wind air speed in miles per hour

From the formula used,

  $3(v_1-v_2)=1800$ Equation 1 $\Rightarrow v_1-v_2=600$

  $2.3(v_1+v_2)=1800$ Equation 2 $\Rightarrow v_1+v_2=782.6$

Add the equations.

  $2v_1=600+782.6$

  $v_1=691.3$

Substituting for $v_1$ ,

  $691.3-v_2=600$

  $v_2=91.3$

Therefore, the air speed of the plane is 691.3 miles per hour and the speed of the wind is 91.3 miles per hour.