SOLUTION: I need some help! can't figure this one out. Was hoping someone could solve for me and show me the steps! Thank you! an airplane flies 520 km against the wind and 680 km with th

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Question 770517: I need some help! can't figure this one out. Was hoping someone could solve for me and show me the steps! Thank you!
an airplane flies 520 km against the wind and 680 km with the wind in a total time of 4 hours. The speed of the airplane in still air is 300 km/h. what is the speed of the wind?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Analyzing in general: w = wind speed; r = speed of plane in no wind. f = distance gone with the wind; b = distance gone against the wind; h = total time in hours flown. Assume time values are unknown but h IS known. Also assume w wind speed is unknown.

WAY________RATE_______________TIME____________DISTANCE
WITH_______r+w________________(__)____________f
AGAINST____r-w________________(__)____________b
Total___________________________h

Using r*t=d we find that any t=d/r.
r is rate, t is time, d is distance.

WAY________RATE_______________TIME____________DISTANCE
WITH_______r+w________________(f%2F%28r%2Bw%29)____________f
AGAINST____r-w________________(b%2F%28r-w%29)____________b
Total___________________________h

Form the time equation, highlight%28f%2F%28r%2Bw%29%2Bb%2F%28r-w%29=h%29 and solve for w, the wind speed, here assumed the unknown variable. Note, the simplest common denominator for handling arithmetic steps is %28r%2Bw%29%28r-w%29.