Chapter 3.6, Problem 14P

To determine

To find:thewind speed and the distance between Abbot and Blair.

Answer to Problem 14P

The wind speed is 15 miles per hour and the distance between Abbot and Blair is 330 miles.

Explanation of Solution

Given information:

With a trial wind, the speed of the plane is 150 mi/h from Abbot to Blair in 2h.

On the return trip against the same wind, the plane was still 60 mi form Abbot after two hours.

Calculation:

Let x be the speed of the wind.

With a tail wind, the ground speed is $150+x$ .

With a head wind, the ground speed is $150-x$ .

Note that, the distance traveled by plane is multiplication of ground of speed and time.

Since the plane traveled in 2h with trial wind, the distance $\text{D =}\left(150+x\right)2$ .

On the return trip against the same wind, the plane was still 60 mi form Abbot after two hours.

The distance, $\text{D =}\left(150-x\right)2+60$

Substitute $\text{D =}\left(150+x\right)2$ in $\text{D =}\left(150-x\right)2+60$ and find the value of x ,

  $\begin{array}{l}\left(150+x\right)2=\left(150-x\right)2+60\\ 300+2x=300-2x+60\\ 2x+2x=300-300+60\\ 4x=60\\ x=15\end{array}$

Thus, the wind speed is 15 miles per hour.

The distance between Abbot and Blair is computed as follows,

Substitute 15 for x in $\text{D =}\left(150+x\right)2$ ,

  $\begin{array}{l}\text{D =}\left(150+15\right)2\\ \text{D =165}\left(2\right)\\ \text{D =330}\end{array}$

Thus, the distance between Abbot and Blair is 330 miles.

Therefore, the wind speed is 15 miles per hour and the distance between Abbot and Blair is 330 miles.