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?
:
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 = 2{{{1/3}}} mph is the rate of the wind
find the speed of the bird
s = 2{{{1/3}}} + 14
s = 16{{{1/3}}} mph is the speed of the bird.