SOLUTION: 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

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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?
Found 2 solutions by ankor@dixie-net.com, jorel555:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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
- = 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
----------------------------
travel time diff: 3 hrs

Answer by jorel555(1290) (Show Source):
You can put this solution on YOUR website!
Let w be the wind speed. Then:
800/160+r +3=800/160-r
800(160-r)+3(25600-r^2)=800(160+r)
128000-800r+76800-3r^2=128000+800r
3r^2+1600r-76800=0
Using the quadratic formula, we get r=44.317,-577.65
Throwing out the negative result, we get the wind velocity as 44.317 mph!!!!!!!!