SOLUTION: A plane flies roundtrip between Great Hall and Bradford. The trip is 150 miles each way. The trip with the wind​ (the wind going in the same​ direction) takes 2.5 &#820

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Question 1086594: A plane flies roundtrip between Great Hall and Bradford. The trip is 150 miles each way. The trip with the wind​ (the wind going in the same​ direction) takes 2.5 ​hours, while the trip against the wind takes 3 hours. What is the speed of the plane in still​ air? What is the speed of the​ wind?
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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The equations are

u - v = 150%2F3,     (1)   (effective speed flying against the wind)
u + v = 150%2F2.5.     (2)   (effective speed flying with the wind)

where "u" is the plane' speed at no wind and "v" is the speed of wind.


Simplify (1) and (2):

u - v = 50,      (3)
u + v = 60.      (4)

Add equations (3) and (4). You will get

2u = 110  ---->  u = 110%2F2 = 55.


Thus we found the speed of the plane at no wind. It is 55 mph.


Now from equation (4)  v = 60 - 55 = 5 mph.


Answer.  The speed of the plane at no wind is 55 mph.  The speed of wind is 5 mph.

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.

In these lessons you will find the detailed solutions of many similar problems.


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".