SOLUTION: Over thanksgiving break, drew decides to fly home from Arcata airport. The pilot announces that they have a tailwind and thus will make the 300 mile flight to San Fransisco airport

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Question 522652: Over thanksgiving break, drew decides to fly home from Arcata airport. The pilot announces that they have a tailwind and thus will make the 300 mile flight to San Fransisco airport in 45 minutes. Unfortunately, coming home, the pilot announces over the intercom that there is a headwind and they will be taking an hour and a half to get to Arcata Airport. How fast is the tailwind/headwind and how fast is Drew's airplane?
Answer by ankor@dixie-net.com(22740) (Show Source):
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Over thanksgiving break, drew decides to fly home from Arcata airport.
The pilot announces that they have a tailwind and thus will make the 300 mile flight to San Fransisco airport in 45 minutes.
Unfortunately, coming home, the pilot announces over the intercom that there is a headwind and they will be taking an hour and a half to get to Arcata Airport.
How fast is the tailwind/headwind and how fast is Drew's airplane?
:
Let s = plane speed in still air
Let w = wind speed
:
Change 45 min to .75 hrs
:
Write a distance equation for each way. (dist = speed * time)
:
.75(s + w) = 300
1.5(s - w) = 300
Simplify both equations, divide the 1st by .75 and the 2nd by 1.5, results
s + w = 400
s - w = 200
-------------Adding eliminates w, find s
2s + 0 = 600
s =
s = 300 mph is the speed of the plane
:
Find the wind speed
300 + w = 400
w = 400 - 300
w = 100 mph is the speed of the wind
:
:
Check solution in the 2nd equation
1.5(300 - 100) =
1.5(200) = 300