Question 91645
I ASSUME THAT YOU ARE LOOKING FOR THE SPEED OF THE WIND
Let x=speed of the wind

distance(d)=rate(r) times time(t) or d=rt; r=d/t and t=d/r

rate against the wind =153-x
amount of time the plane travels against the wind=849/(153-x) 
rate with the wind=153+x
amount of time the plane travels with the wind=1402/(153+x) 


Now we know that the amount of time the plane travels with the wind plus the amount of time the plane travels against the wind=16 hrs.  So our equation to solve is:

1402/(153+x)+849/(153-x)=16  multiply each term by (153+x)(153-x) to get rid of fractions

1402(153-x)+849(153+x)=16(153+x)(153-x)  get rid of parens

214506-1402x+129897+849x=374544-16x^2  add 16x^2 and subtract 374544 from both sides

214506-374544+16x^2-1402x+129897+849x=374544-374544+16x^2-16x^2 collect like terms

16x^2-553x-30141=0  Quadratic in standard form.  Solve using the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (553 +- sqrt( (-553)^2-4*16*(-30141) ))/(2*16) }}} 
{{{x = (553 +- sqrt( ( 2234833))/(32)) }}} 
{{{x = (553 +- 1494.94)/(32)) }}} 
{{{x = (553 + 1494.94)/(32)) }}} 
{{{x=63.998= 64}}} mph----------------------------speed of wind
and
{{{x = (553 - 1494.94)/(32)) }}} discount negative value for speed of wind

CK 

1402/(153+64)+849/(153-64)=16 
1402/217+ 849/89=16
6.46+9.54=16
15.9993~~~~~~16   Hope this helps----ptaylor