SOLUTION: A plane travels at a speed of 205 MPH in still air. Flying with a tailwind, the plane is clocked over a distance of 950 miles. Flying against a headwind, it takes 2 hours longer to

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Question 1103790: A plane travels at a speed of 205 MPH in still air. Flying with a tailwind, the plane is clocked over a distance of 950 miles. Flying against a headwind, it takes 2 hours longer to complete the return trip. what was the wind velocity?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
A plane travels at a speed of 205 MPH in still air. Flying with highlight%28cross%28a_tailwind%29%29 the wind, the plane is clocked over a distance of 950 miles.
Flying against highlight%28cross%28a_headwind%29%29 the wind, it takes 2 hours longer to complete the return trip. what was the highlight%28cross%28wind+_velocity%29%29 speed of the wind ?
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Let v = the wind speed (in miles per hour), now unknown.


The  the tailwind speed = 205 + v miles per hour.

         Headwind speed = 205 - v miles per hour.


"Time equation"

950%2F%28205-v%29 - 950%2F%28205%2Bv%29 = 2  hours.

950*(205+v) - 950*(205-v) = 2*(205^2-v^2)

2*950*v = 2*(205^2-v^2),

950v = 205^2 - v^2

v^2 + 950v - 205^2 = 0

v%5B1%2C2%5D = %28-950+%2B-+sqrt%28950%5E2%2B4%2A205%5E2%29%29%2F2 = %28-950+%2B-+1034.7%29%2F2.


Only positive root makes sense:  v =  %28-950+%2B+1034.7%29%2F2 = 42.35 mph.


Answer.  The speed of the wind is 42.35 mph.


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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.

In these lessons you will find the detailed solutions of many similar problems.
Consider them as samples.  Read them attentively.
In this way you will learn how to solve similar problems once and for all.


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.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A plane travels at a speed of 205 MPH in still air. Flying with a tailwind, the plane is clocked over a distance of 950 miles. Flying against a headwind, it takes 2 hours longer to complete the return trip. what was the wind velocity?
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tailwind and headwind are the commonly used terms in aviation.
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"with a tailwind" borders on redundancy because it's flying "with the wind."
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"against a headwind" is redundant, but not seriously.
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"wind velocity" is not correct, it's wind speed.
Velocity is a vector that includes speed and direction, not just speed.
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205 MPH in still air - "in still air" is the airspeed of the plane.
Planes don't use MPH, or miles/hour. They use knots.
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You never outgrow your need for useless facts.