Chapter 9.6, Problem 31PPS

To determine

To find : what is the average speed of the wind during the flight

Answer to Problem 31PPS

The average speed of the wind is $55.5\text{ hours}$ during the flight

Explanation of Solution

Given information :

It takes a plane 20 hours to fly to its destination against the wind. The return trip takes 16 hours. If the plane’s average speed in still air is 500 miles per hours.

Formula used : $\text{distance}=\text{ rate }\times \text{ time}$

Calculation :

Let $w$ be the speed of wind

The time of the destination against the wind $\text{=20 hours}$

The rate of the destination against the wind $\text{=}\left(500-w\right)$

Therefore, the distance of its destination against the wind $\text{=}\left(500-w\right)20$

The time of the return trip $\text{=16 hours}$

The rate of the return trip $\text{=}\left(500+w\right)$

Therefore, the distance of the return trip $\text{=}\left(500+w\right)16$

Therefore,

  $\begin{array}{l}\left(500-w\right)20=(500+w)16\\ 10000-20w=8000+16w\\ 20w+16w=10000-8000\\ 36w=2000\\ w=\frac{2000}{36}\\ w=55.5\text{ hours}\end{array}$

Therefore, the average speed of the wind is $55.5\text{ hours}$ during the flight.

Hence, the average speed of the wind is $55.5\text{ hours}$ during the flight.