SOLUTION: A student group flies to Cancun for spring break, a distance of 1200 miles. The plane used for both trips has an average cruising speed of 300 miles per hour in still air. The trip

Question 1114311: A student group flies to Cancun for spring break, a distance of 1200 miles. The plane used for both trips has an average cruising speed of 300 miles per hour in still air. The trip down is with the prevailing winds and takes 1 1/2 hours less than the trip back, against the same strength wind. What is the wind speed?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
distance of 1200 miles
plane speed = 300 mph in still air
The trip down is with the prevailing winds and takes 1 1/2 hours less than the trip back,
Trip down takes less time so plane flies with wind
Return against wind
down - speed = 300 +x
time taken = 1200/(300+x)
return speed = 300-x
time taken = 1200/(300-x)
Return time - down time = 1.5 hours

((1200(300+x))-(1200*(300-x))/((300+x)(300-x)))=1.5

360000+1200x -360000+1200x/(90000-x^2)=1.5
2400x= 1.5(90000-x^2)

2400x = 135000-1.5x2

1.5x^2+2400x -135000=0
solve
x= 54.4 mph wind speed
Check
(1200/(300-54.4))- (1200/(354.4))=1.49999

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