Question 1120070: A man flies a small airplane from Fargo to Bismarck, North Dakota a distance of 180 miles. Because he is flying into a headwind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?
Found 3 solutions by ankor@dixie-net.com, greenestamps, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A man flies a small airplane from Fargo to Bismarck, North Dakota a distance of 180 miles.
Because he is flying into a headwind, the trip takes him 2 hours.
On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes.
Change 1 hr 12 min to 1.2 hrs
What is his speed in still air, and how fast is the wind blowing?
:
let s = aircraft speed in still air
let w = speed of the wind
then
(s-w) = effective speed into a headwind
and
(s+w) = effective speed with the wind
:
Write dist equation for each way; (dist = time * speed
2(s-w) = 180
1.2(s+w) = 180
:
Simplify, divide the 1st equatio by 2 and the 2nd equation by 1.2
s - w = 90
s + w = 150
--------------addition eliminates w, find s
2s + 0 = 240
s = 240/2
s = 120 mph the speed in still air
and
12 + w = 150
w = 30 mph is the wind
:
;
Check this; find the distance with these values
2(120-30) = 180
1.2(120+30) = 180
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
The solution can be obtained informally on a path nearly identical to the formal algebraic solution provided by the other tutor.
The average speed against the wind is 180 miles / 2 hours = 90mph. The average speed with the wind is 180 miles / 1.2 hours = 150mph.
One speed is the speed of the airplane plus the speed of the wind; the other is the speed of the airplane minus the speed of the wind.
That is a kind of situation that shows up in many different kinds of problems. Logical analysis says that the speed of the airplane is halfway between the two average speeds; then the wind speed is the difference between the plane's speed and average speed on either of the legs.
Halfway between 90 and 150 is 120. The speed of the airplane is 120mph; the speed of the wind is 150-120 = 120-90 = 30mph.
Answer by josgarithmetic(39616)  (Show Source):
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