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How to solve this speed/distance problem

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an airplane flies 150 miles east, then returns to the airport. The total flight time is 2 hours. The flight to the east is with wind, the flight back is against the wind. The wind is blowing at 25mph. What is the speed of the plane with no wind, to the nearest tenth?

Apr 9th, 2015

Let the speed of the plane with no wind be x mph.

Flight to the east: time = 150/(x+25); flight to the west: time = 150/(x - 25).

The total time is 2, so we get the following equation: 150/(x+25) + 150/(x-25) = 2.

Multiply both parts by x^2 - 625:  150(x-25) + 150(x+25) = 2(x^2 - 625)

300x = 2x^2 - 1250;  2x^2 - 300x - 1250 = 0; x^2 - 150 x - 625 = 0

The solution is x = (150 + sqrt{150^2 + 4*625}) /2 = (150 + sqrt{25000}) / 2 = (150 + 50sqrt{10}) /2 

= 75 + 25sqrt{10} = 154.1 mph. Note the other solution of the quadratic equation is negative 75 - 25sqrt{10} and does not make sense.

Answer: 154.1 mph 

Apr 8th, 2015

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