SOLUTION: A European Swallow flies into the wind from the castle of Uther Penn Dragon to Camelot while carrying a coconut. He flies 28 miles to Camelot in 2 hours, delivers the coconut and

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Question 1166213: A European Swallow flies into the wind from the castle of Uther Penn Dragon to Camelot while carrying a coconut. He flies 28 miles to Camelot in 2 hours, delivers the coconut and retrieves an identical coconut to carry back to the castle. He travels back the same distance (now with a tail wind) in 1.5 hours. What is the air speed of the laden swallow? What is the velocity of the wind?

Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A European Swallow flies into the wind from the castle of Uther Penn Dragon to Camelot while carrying a coconut. He flies 28 miles to Camelot in 2 hours, delivers the coconut and retrieves an identical coconut to carry back to the castle. He travels back the same distance (now with a tail wind) in 1.5 hours. What is the air speed of the laden swallow? What is the velocity of the wind?
:
let s = the bird's speed in still air
let w = the rate of the wind
:
Write a dist equation: dist = time * effective speed
2(s - w) = 28
1.5(s + w) = 28
distribute and simplify the first equation
2s - 2w = 28
divide by 2
s - w = 14
s = w + 14
In the 2nd equation replace s with w+14
1.5((w+14) + w) = 28
1.5(2w + 14) = 28
distribute
3w + 21 = 28
3w = 28 - 21
3w = 7
w = 7/3
w = 21%2F3 mph is the rate of the wind
find the speed of the bird
s = 21%2F3 + 14
s = 161%2F3 mph is the speed of the bird.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A European Swallow flies into the wind from the castle of Uther Penn Dragon to Camelot while carrying a coconut. He flies 28 miles to Camelot in 2 hours, delivers the coconut and retrieves an identical coconut to carry back to the castle. He travels back the same distance (now with a tail wind) in 1.5 hours. What is the air speed of the laden swallow? What is the velocity of the wind?
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The groundspeed upwind is 28/2 = 14 mi/hr
The groundspeed downwind is 28/1.5 = 56/3 mi/hr
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The airspeed is the average of the 2 speeds, = 98/3 mi/hr
The windspeed is the difference between airspeed and either groundspeed.
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PS If the coconuts are identical, what's the point of the trip?