An airplane flies due west (i. e. in the-x direction) between two airports. for one-quarter of the distance it travels at 650.0 km/h and the rest at 750.0 km/h. what is the average velocity (not speed) of the airplane?

average velocity 722 km/h

Explanation:

The average speed is defined with the total distance traveled between the total time, let's look for distance and time, we can use the equation

     V = X / t

 The first distance tells us that it travels ¼ of the total distance (X) at a speed (V1) of 650 km / h

     V1 = X1 / t1

    t1 = X1 / V1

    t1 = ¼ X / 650

The second distance runs ¾ of the total distance at V2 = 750 km / h

    V2 = X2 / t2

    t2 = X2 / V2

    t2 = ¾ X / 750

Total time is the sum of these times

    t all = t1 + t2

    t all = ¼ X / 650 + ¾ X / 750

    t all = X (1/2600 +3/3000)

    t all = X (1/2600 + 1/1000)

Let's calculate the average speed

    V = X / t

    V = X / X (1/2600 +0.001)

    V = 1 / 0.001385

    V = 722 km / h