Question 184013
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Let r=rate of the wind
Then 150+r=plane's rate of travel with the wind
And 150-r=planes rate of travel against the wind
Time travelling with the wind=180/(150+r)
Time travelling against the wind =180/(150-r)
And we are told that the above two times add up to 2.5 hr, so:
180/(150+r)+180/(150-r)=2.5  multiply each term by (150+r)(150-r)
180(150-r)+180(150+r)=2.5(22,500-r^2) divide each term by 2.5
72(150-r)+72(150+r)=22,500-r^2 get rid of parens
10,800-72r+10,800+72r=22,500-r^2 or
21,600-22,500=-r^2
-r^2=-900  multiply each side by -1
r^2=900 take sqrt of each side
r=+or- 30 mi/hr  wind speed is positive,so:
r=30 mph-----------------------rate of the wind
Then 150+r=150+30=180 mph-----plane's rate of travel with the wind
And 150-r=150-30=120 mph ----planes rate of travel against the wind

CK
180/180+180/120=2.5
1+1.5=2.5
2.5=2.5

Hope this helps---ptaylor