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Algebra problem ????? word to anyone

a pilot enterprises must travel from the headquarters of the company to a manufacturing plant and back in 4 hours. the distance between headquarters and plants in 300mi. if there is a headwind and a 20 mph tailwind going back 20 mph, the speed with which the aircraft must be able to travel in the air yet ??????????????? please explain?

Let s = speed of the plane in still air. Using the ratio of the distance / Speed = time, we know that the distance is 300 miles each way and total time is 4 hours. The speed is reduced by 20 mph and 20 mph will increase in return. (Time to go) + (Next time) = 4 hours. As time goes = (300) / (s – 20) and the time to come = (300) / (s + 20), (300) / (s – 20) + (300) / (s + 20) = 4. Multiplying by (s – 20) * (s + 20) yields 300 * (s + 20) + 300 * (s – 20) = 4 * (s – 20) * (s + 20) 600 = 4 * (s ^ 2 – 400) 4s ^ 2 – 600 – 1600 = 0. Divide by 4 yields s ^ 2 – 125cc – 400 = 0, a quadratic equation. Obtained using the quadratic formula s = (- (-125) ± √ ((-125) ^ 2 – 4 * 1 *- 400)) / (2 * 1) = (125 ± √ (15625 1600)) / 2 = 128.1 or -3.1 Since we know that the speed can not be negative, the speed of the airplane in still air is about 128.1 mph.

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