Hello, SwissArmelle!

I'll do it the "standard" way", but we'll get a tricky equation . . .

We will use: .During a 3000-mile flight, a plane encountered a strong tail wind

that increased its speed by 100 mi/hour.

This increase of speed shortened the flying time by one hour.

Find the speed of the plane relative to the ground.

Let = speed of the plane (ground speed).

Normally, it would fly the 3000 miles at mph.

. . It would take: . hours.

With the tailwind, its speed is mph.

. . To fly 3000 miles, it took only: . hours.

And this is one hour less than its normal time.

There is our equation . . . .

Multiply by

This simplifies to the quadratic: .

. . which factors: .

. . and has roots: .

Therefore, the plane's ground speed is: