SOLUTION: an airplane can fly at an average of 425 kph in still air. if the plane flies 900 km with a constant wind blowing and returns to fly against the wind in a total time of 4 hours and

Question 899803: an airplane can fly at an average of 425 kph in still air. if the plane flies 900 km with a constant wind blowing and returns to fly against the wind in a total time of 4 hours and 15 minutes, what must be the velocity of the wind?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
an airplane can fly at an average of 425 kph in still air.
if the plane flies 900 km with a constant wind blowing and returns to fly against the wind in a total time of 4 hours and 15 minutes,
what must be the velocity of the wind?
:
Change 4 hrs 15 min to 4.25 hrs
:
let w = the velocity of the wind
then
(425+w) = ground speed with the wind
and
(425-w) = ground speed against the wind
;
Write a time equation; time = dist/speed
Time out + return time = 4.25 hrs
+ = 4.25
multiply equation by (424+w)(425-w), cancel the denominators and you have
900(425-w) + 900(425-w) = 4.25(425-w)(425+w)
382500 - 900w + 382500 + 900w = 4.25(180625-w^2)
765000 = 4.25(180625-w^2)
divide both sides by 4.25
180000 = 180625 - w^2
w^2 = 180625 - 180000
w^2 = 625
w =
w = 25 km/hr is the velocity of the wind
:
See if that checks out, find the actual time each way
900/450 = 2 hrs
900/400 = 2.25 hrs
----------------------
total time: 4.25 hrs
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