Question 98799
distance(d)=rate(r) times time(t) or d=rt; t=d/r and r=d/t
Let r=rate (speed) of plane in still air

time going =720/(r-30)
time returning=720/(r+30)
(Note: if  the plane is flying against the wind, then we must subtract the wind speed from the planes speed in still air. If it flying with the wind then we add)

Now we are told that the time going + time returning=10 h, so:

720/(r-30)+720/(r+30)=10 multiply each term by (r-30)(r+30)

720(r+30)+720(r-30)=10(r-30)(r+30) get rid of parens

720r+21600+720r-21600=10r^2-9000  subtract 10r^2 and add 9000 to both sides

-10r^2+1440r+9000=0  divide each term by -10
r^2-144r-900=0  quadratic in standard form and it can be factored

(r+6)(r-150)=0
discount negative value --in this problem rate of speed is positive

r=150---------------------rate (speed) of plane in still air


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

6 h + 4 h=10 h
10 h=10 h


Hope this helps---ptaylor