Aplane travels speed at 225 mph in still air. flying with tailwind, the plane is clocked over distance of 875 miles. flying against headwind, it takes 1 hour longer to complete the return trip. what is the wind velocity?

The wind speed is 28.466 mi/h

Step-by-step explanation:

Let's call Vs=225mi/h the plane speed in still air. Let's have X=875 mi the distance traveled

We'll also call Vw the wind speed. In the first flight, the plane goes with a speed of Vs+Vw.

The return trip is made flying against a headwind with a speed of Vs-Vw

The time taken to travel X miles with a tailwind is

The time taken to travel X miles with a headwind is

We know because the return trip is 1 hour longer. Then we have

Multiplying by (Vs+Vw)(Vs-Vw)

Replacing the values of X=875 and Vs=225 we reach a second-degree equation

Which has the following roots:

Vw=28.466, Vw=-1778.466

We take the positive root and conclude

The wind speed is 28.466 mi/h

Note: We can easily check that the first time is 3.45h and the second time is 4.45h.

ab will be equal to

24 units

step-by-step explanation: