Question 183141
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Let s=speed of plane in still air
And let r=speed of the wind
s+r=plane speed with the wind 
s-r=plane speed against the wind.  We are told that:
s+r=(s-r)+30  subtract s from and add r to each side
2r=30
r=15 mph speed of wind
time against the wind=520/(s-15)
time with the wind=520/(s+15)
And we are told that time with wind + time against wind =8.8 hr, so:
520/(s-15) + 520/(s+15)=8.8  multiply each term by (s-15)(s+15)
520(s+15)+520(s-15)=8.8(s-15)(s+15) get rid of parens
520s+7800+520s-7800=8.8s^2-1980 simplify
1040s-8.8s^2+1980=0 or
8.8s^2-1040s-1980=0----------------quadratic in standard form.  Solve using the quadratic formula:
{{{s = (-b +- sqrt( b^2-4*a*c ))/(2*a)}}}
{{{s = (1040 +- sqrt( (1040)^2-4*(8.8)*(-1980) ))/(2*(8.8))}}}
{{{s = (1040 +- sqrt(1081600+69696 ))/(17.6)}}}
{{{s = (1040 +- sqrt( 1151296))/(17.6)}}}
{{{s = (1040 +- (1072.98))/(17.6)}}}

Disregard negative value for s, speed is positive
{{{s = (1040 +(1072.98))/(17.6)}}}
{{{s = 120.1}}}mph---------------------speed of plane in still air

CK
520/(120.1+15) +520/(120.1-15)=8.8
3.849+4.95=8.8
~~~~8.8=8.8


Hope this helps---ptaylor