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?
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

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


Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.
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.

----------------
It is a typical "tailwind and headwind" word problem.

See the lessons
    - Wind and Current problems
    - Wind and Current problems solvable by quadratic equations
    - Selected problems from the archive on a plane flying with and against the wind
in this site.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the section "Word problems",  the topic "Travel and Distance problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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