Question 83265

Let x=speed (rate) of the plane in still air
speed against headwind =x-30
speed with headwind=x+30

Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Time required travelling against the headwind=720/(x-30)
Time require travelling with the headwind=720/(x+30)

Now we are told that the total time was 10 hours, So:

720/(x-30)+720/(x+30)=10  multiply both sides by (x-30)(x+30)

720(x+30)+720(x-30)=10(x-30)(x+30)  divide both sides by 10

72(x+30)+72(x-30)=(x-30)(x+30)   get rid of parens

72x+2160+72x-2160=x^2-900  collect like terms

144x=x^2-900  subtract 144x from both sides

144x-144x=x^2-144x-900  simplify

x^2-144x-900=0   quadratic in standard form and this can be factored

(x-150)(x+6)=0

x=150mph-------------------------------------rate in still air
x=-6----------------discount negative value for speed

CK

720/(150-30)+720/(150+30)=10

6+4=10
10=10


Hope this helps---ptaylor