A plane is traveling at a speed of 160 mph in still air. Flying with a tail wind, the plane is clocked over a distance of 800 miles. Flying against a headwind it takes 3 more hours to complete the return trip. What was the wind velocity?

Question

A plane is traveling at a speed of 160 mph in still air.  Flying with a tail wind, the plane is clocked over a distance of 800 miles. Flying against a headwind it takes 3 more hours to complete the return trip. What was the wind velocity?

Reiny · Answer

wind speed ---- x mph
speed going with the wind = 160+x
speed going against the wind = 160-x

800/(160-x) - 800(160+x) = 3
times (160-x)(160+x)
800(160+x) - 800(160-x) = 3(160+x)(160-x)
800x + 800x = 76800 - 3x^2
3x^2 + 1600x - 76800 = 0
x = (-1600 ± √3481600)/6
x = appr 44.3 mph or some negative x

The speed of the wind is appr 44.3 mph

check:
800/115.7 - 800/204.3
= 2.9986 , not bad