Word problem

Question

A plane travels 800 mi from Dallas, Texas, to Atlanta, Georgia, with a prevailing west wind of 40 mph. The return trip against the wind takes 1/2 hr longer. Find the average speed of the plane in still air.

Answer 1

Let x = speed of plane in still air

 

Speed against the wind = x - 40

Speed with the wind = x + 40

 

Distance = (rate)(time), so time = distance/rate

 

Time to Dallas = Time from Dallas + 1/2

 

800/(x-40) = 800/(x+40) + 1/2

 

Multiply the equation by the LCD, 2(x-40)(x+40)

 

1600(x+40) = 1600(x-40) + (x+40)(x-40)

 

1600x + 64000 = 1600x - 64000 + x² - 1600

 

x² - 129600= 0

 

(x - 360)(x + 360) = 0

 

x = 360 or x = -360

 

Since the speed of the plane can't be negative, 

 

x = 360 mph