SOLUTION: A plane travels at a speed of 180 mph in still air . Flying with a tailwind the plane is clocked over a of distance of 900 miles. Flying against a headwind it takes 2 hours longer

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Question 1103240: A plane travels at a speed of 180 mph in still air . Flying with a tailwind the plane is clocked over a of distance of 900 miles. Flying against a headwind it takes 2 hours longer to complete the return trip. What was the wind velocity?
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
system%28r=180%2Cd=900%2Ch=2%2Cw=unknownWindSpeed%29
h is for time difference 
                  SPEEDS   TIMES      DISTANCE

WITH WIND          r+w     d/(r+w)      d

AGAINST WIND       r-w     d/(r-w)      d

DIFFERENCE                  h

highlight_green%28d%2F%28r-w%29-d%2F%28r%2Bw%29=h%29
Solve for w.
d%28r%2Bw%29-d%28r-w%29=h%28r%5E2-w%5E2%29
dr%2Bdw-dr%2Bdw=hr%5E2-hw%5E2
hw%5E2%2B2dw-hr%5E2=0
Using general solution for quadratic equation, and not assuming the quadratic would be factorable,

w=%28-2d%2B-+sqrt%28%282d%29%5E2%2B4h%2Ahr%5E2%29%29%2F%282h%29

w=%28-2d%2B-+sqrt%284d%5E2%2B4h%5E2r%5E2%29%29%2F%282h%29

highlight%28w=%28-d%2B-+sqrt%28d%5E2%2Bh%5E2r%5E2%29%29%2Fh%29-------the PLUS form will probably be what you want. Substitute the given values now and evaluate both solutions for w, and decide which makes sense.

Substitute the given values into the formula for w, and should find highlight%28w=34.7%2A%28miles%2Fhour%29%29.