Question 33306
Plane total distance = 720 miles:
With the wind the plane speed is: x+30
Against the wind: x-30
Total time of them both = 10h
equation:
{{{720/(x-30)+720/(x+30)=10}}}
720[(x-30)+(x+30)]=10[(x-30)(x+30)]
720(2x)=10(x^2-900)
10x^2-9000-1440x=0
x^2-144x-900=0
{{{x^2-144x-900=0}}}
Use quadratic formula: {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
in {{{ax^2+bx+c}}} a=1, b=-144, c=-900
{{{x=(-(-144)+-sqrt((-144)^2-4(1)(-900)))/ 2 * (1))}}} -->DIVIDE BY 2
{{{x=(144+-sqrt(24336))/ 2}}} ---> 
{{{x=(144+-156)/(2)}}}
Add:
{{{x=144+156/(2)}}}
x=150


Hence the speed of the plane in still air is 150mi/h.
Paul.