Question 1039246
 A plane travels at a speed of 160 mph in still air.
 Flying with a tailwind the plane is clocked over a distance of 800 miles.
 Flying against a headwind, it takes 3 hours longer to complete the return trip.
 What was the wind velocity?
:
let w = the velocity of the wind
then
(160+w) = the effective speed with the wind
and
(160-w) = the effective speed against 
:
Write a time equation; time = dist/speed
Against time - with time = 3 hr
{{{800/((160-w))}}} - {{{800/((160+w))}}} = 3
Multiply equation by (160-w)(160+w), cancel the denominators
800(160+w) - 800(160-w) = 3(160-w)(160+w)
128000 + 800w - 128000 + 800w = 3(25600-w^2)
1600w = 76800 - 3w^2
Form a quadratic equation on the left
3w^2 + 1600w - 76800 = 0
Use the quadratic formula to find w: a=3; b=1600; c=-76800
I got a positive solution of
w = 44.32 mph is the speed of the wind
:
:
Check this by finding the actual time each way
800/(160-44.32) = 6.915 hrs
800/(160+44.32) = 3.915 hrs
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travel time diff: 3 hrs