Question 24178
Let the plane's speed be x
Agianst the headwind = x-30
With the headwind = x+30
total time = 10h


{{{720/x-30 + 720/x+30 = 10}}}
720[(x-30)+(x+30)]=10[(x-30)(x+30)] --> simplify
{{{720[2x]=10[x^2-900]}}}
{{{1440x=10x^2-9000}}}
Quardrtic equation: {{{10x^2-1440x-9000 = 0}}} --> divide the equation by 10
{{{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 x (1))}}} -->DIVIDE BY 2
{{{x=144+-sqrt(24336))/ 2}}} ---> DIVIDE by 2.
{{{x=144+-156/(2)}}}
Add:
{{{x=144+156/(2)}}}
x=150


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