Question 1175107: When small airplane flies with the wind, it can travel 450 miles per 3 hours. When the
same airplane flies in the opposite direction against the wind, it takes 5 hours to cover the
same distance. Find the average speed of the airplane in still air. Find the average speed of the wind.
Answer by ikleyn(52798)   (Show Source):
You can put this solution on YOUR website! .
Flying with the wind, the airplane has the effective speed
u + v = 450/3 = 150 miles per hour, (1)
where u is the speed of the airplane at no wind and v is the speed of wind.
Flying against the wind, the airplane has the effective speed
u - v = 450/5 = 90 miles per hour (2)
Adding equations (1) and (2), you get
2u = 150 + 90 = 240 mph,
u = 240/2 = 120 mph.
Then the air speed, from equation (1), is v = 150-120 = 30 mph.
ANSWER. The average speed of the airplane is 120 miles per hour.
The speed of the wind is 30 miles per hour.
Solved.
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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, where you will find other similar solved problems with detailed explanations.
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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