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 . . . .
This simplifies to the quadratic: .
. . which factors: .
. . and has roots: .
Therefore, the plane's ground speed is: