John flies from Atlanta, Georgia to San Francisco, California. It takes 5.6 hours to travel 2100 miles against the head wind. At the same time, Debby flies from San Francisco to Atlanta. Her plane travels with the same average airspeed, but the tail wind, and her flight takes only 4.8 hours. Write a system of equation that relate time, airspeed, and wind speed to distance for each traveler. Solve the system to fine the air speed

The average airspeed of the two planes is .

Step-by-step explanation:

Let denotes the average airspeed (in miles-per-hour) of the two planes. Let denote the average speed of wind (also in miles-per-hour) along that route.

John is travelling against the head wind. Therefore, his ground speed would be the difference between his airspeed and the speed of the wind. That is:

.

On the other hand, Debby is travelling in the tail wind. Assume that Debby and John are taking the same route but in the opposite directions. The ground speed of Debby would be the sum of her airspeed and the speed of the wind:

.

Keep in mind that:

.

This equation can help relate time and ground speed to distance.

John traveled miles in hours at a ground speed of . Therefore:

.

Similarly, Debby traveled miles in hours at a ground speed of . Therefore:

.

Combine these two equations to obtain:

.

Solve this system of equations for and :

.

In other words:

29933333.33

step-by-step explanation: