Chapter 11.1, Problem 62AYU

To determine

To find: The average airspeed of a single- engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?

Answer to Problem 62AYU

Solution:

The average wind speed is 30 mph.

Explanation of Solution

Given:

The average airspeed of a single- engine aircraft is 150 miles per hour. The aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind.

Calculation:

Let the distance be $x$ .

It is given that average airspeed is 150 miles per hour.

For with the wind is given by,

Rate = speed/time

We have, Rate $=\frac{x}{2}\text{mph}$

For against the wind is given by,

Rate = speed/time

We have, Rate $=\frac{x}{2}\text{mph}$

Average Airspeed $=\frac{\frac{x}{2}+\frac{x}{2}}{2}=\frac{5x}{6}$$150=\frac{5x}{6}$

  $x=360$ miles

For with the wind is given by,

Rate $=\frac{360}{2}\text{mph}=180\text{mph}$

For against the wind is given by,

Rate $=\frac{360}{3}\text{mph}=120\text{mph}$

Average wind speed $=\frac{120-120}{2}=30\text{mph}$

Therefore, the average wind speed is 30 mph.