SOLUTION: The bird capable of the fastest flying speed is the swift. A swift flying with the wind to a favorite feeding spot traveled 42 mi in 0.3 h. On returning, now against the wind, the
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Question 1115176: The bird capable of the fastest flying speed is the swift. A swift flying with the wind to a favorite feeding spot traveled 42 mi in 0.3 h. On returning, now against the wind, the swift was able to travel only 33 mi in the same amount of time. What is the rate of the swift in calm air, and what was the rate of the wind?
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Bird speed= x km/h
wind speed= y km/h
with wind speed= (x+y)
against wind speed (x-y)
d= 42 with wind
42 / (x+y) = 0.3
divide by 0.3
140 / (x+y) = 1
(x+y) = 140 ............1
d= = 33 against wind
33/(x-y) = 0.3
divide by 0.3
110 /(x-y) = 1
x - y = 110 .............2
add up (1) & (2)
2 x = 250
/ 2
x= 125 mph speed of Plane in still air
plug value of x in (1)
we get y= 15 mph speed of wind
Let u = the rate of the swift in calm air (mi/h), and
let v = the rate of the wind/
Then
= 140 = u + v is the effective tailwind speed, and
= 110 = u - v is the effective speed against the wind.
Adding the equation, you get
2u = 140 + 110 = 250 ====> u = = 125 mi/h the rate of the swift in calm air, and
v = 140-u = 140-125 = 15 mi/h for the rate of wind.
Solved.
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It is a typical "tailwind and headwind" word problem.
