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a plane flew 720 mi in 3 hr with the wind. it would take 4 hr to travel the same distance against the wind.
what is the rate of the plane at no wind and the rate of wind?
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Let "u" be the speed of the plane at no wind, in mph.
Let "v" be the speed of wind.
Then the effective speed of the plane flying WITH the wind is (u+v) mph (relative to the ground).
the effective speed of the plane flying AGAINST the wind is (u-v) mph (relative to the ground).
According to the condition,
the plane effective speed is = 240 mph flying with the wind,
and effective speed is = 180 mph flying against the wind.
It gives you two equations
u + v = 240, (1)
u - v = 180. (2)
To solve the system, add the two equations (both sides). You will get
2u = 240 + 180 = 420. Hence, u = = 210.
Thus the speed of the plane at no wind is 210 miles per hour.
Next, from the equation (1) v = 240 - u = 240 - 210 = 30 miles per hour.
Thus the speed of the wind is 30 miles per hour.
Answer. The speed of the plane at no wind is 210 miles per hour.
The speed of the wind is 30 miles per hour.
Check. The speed of the plane with the wind is 210 + 30 = 240 mph, and the flight time is = 3 hours.
The speed of the plane against the wind is 210 - 30 = 180 mph, and the flight time is = 4 hours.
Checks !
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.
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".